A228915 -id:A228915 - cp's OEIS frontend

A052224 Numbers whose sum of digits is 10.

19, 28, 37, 46, 55, 64, 73, 82, 91, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 208, 217, 226, 235, 244, 253, 262, 271, 280, 307, 316, 325, 334, 343, 352, 361, 370, 406, 415, 424, 433, 442, 451, 460, 505, 514, 523, 532, 541, 550, 604, 613, 622, 631, 640

Offset: 1

Henry Bottomley, Feb 01 2000

Proper subsequence of A017173. - Rick L. Shepherd, Jan 12 2009
Subsequence of A227793. - Michel Marcus, Sep 23 2013
A007953(a(n)) = 10; number of repdigits = #{55,22222,1^10} = A242627(10) = 3. - Reinhard Zumkeller, Jul 17 2014
a(n) = A094677(n) for n = 1..28. - Reinhard Zumkeller, Nov 08 2015
The number of terms having <= m digits is the coefficient of x^10 in sum(i=0,9,x^i)^m = ((1-x^10)/(1-x))^m. - David A. Corneth, Jun 04 2016
In general, the set of numbers with sum of base-b digits equal to b is a subset of { (b-1)*k + 1; k = 2, 3, 4, ... }. - M. F. Hasler, Dec 23 2016

Rémy Sigrist, Table of n, a(n) for n = 1..10000 (first 3921 terms from T. D. Noe)

Cf. A007953, A017173, A228915, A254524.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A242614, A242627.
Cf. A094677.
Cf. A018900, A187813.
Sum of base-b digits equal b: A226636 (b = 3), A226969 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9).

a052224 n = a052224_list !! (n-1)
a052224_list = filter ((== 10) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1000] | &+Intseq(n) eq 10 ]; // Vincenzo Librandi, Mar 10 2013

sd := proc (n) options operator, arrow: add(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: a := proc (n) if sd(n) = 10 then n else end if end proc: seq(a(n), n = 1 .. 800); # Emeric Deutsch, Jan 16 2009

Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 7]], {s, Rest[IntegerPartitions[10]]}]]] (* T. D. Noe, Mar 08 2013 *)
Select[Range[1000], Total[IntegerDigits[#]] == 10 &] (* Vincenzo Librandi, Mar 10 2013 *)

isok(n) = sumdigits(n) == 10; \\ Michel Marcus, Dec 28 2015

\\ This algorithm needs a modified binomial.
C(n, k)=if(n>=k, binomial(n, k), 0)
\\ ways to roll s-q with q dice having sides 0 through n - 1.
b(s, q, n)=if(s<=q*(n-1), s+=q; sum(i=0, q-1, (-1)^i*C(q, i)*C(s-1-n*i, q-1)), 0)
\\ main algorithm; this program applies to all sequences of the form "Numbers whose sum of digits is m."
a(n,{m=10}) = {my(q); q = 2; while(b(m, q, 10) < n, q++); q--; s = m; os = m; r=0; while(q, if(b(s, q, 10) < n, n-=b(s, q, 10); s--, r+=(os-s)*10^(q); os = s; q--)); r+= s; r}
\\ David A. Corneth, Jun 05 2016

from sympy.utilities.iterables import multiset_permutations
def auptodigs(maxdigits, b=10, sod=10): # works for any base, sum-of-digits
    alst = [sod] if 0 <= sod < b else []
    nzdigs = [i for i in range(1, b) if i <= sod]
    nzmultiset = []
    for d in range(1, b):
        nzmultiset += [d]*(sod//d)
    for d in range(2, maxdigits + 1):
        fullmultiset = [0]*(d-1-(sod-1)//(b-1)) + nzmultiset
        for firstdig in nzdigs:
            target_sum, restmultiset = sod - int(firstdig), fullmultiset[:]
            restmultiset.remove(firstdig)
            for p in multiset_permutations(restmultiset, d-1):
              if sum(p) == target_sum:
                  alst.append(int("".join(map(str, [firstdig]+p)), b))
                  if p[0] == target_sum:
                      break
    return alst
print(auptodigs(4)) # Michael S. Branicky, Sep 14 2021

def A052224(N = 19):
    """Return a generator of the sequence of all integers >= N with the same
    digit sum as N."""
    while True:
        yield N
        N = A228915(N) # skip to next larger integer with the same digit sum
a = A052224(); [next(a) for  in range(50)] # _M. F. Hasler, Mar 16 2022

a(n+1) = A228915(a(n)) for any n > 0. - Rémy Sigrist, Jul 10 2018

Incorrect formula deleted by N. J. A. Sloane, Jan 15 2009
Extended by Emeric Deutsch, Jan 16 2009
Offset changed by Bruno Berselli, Mar 07 2013

A107579 Primes with digit sum 10.

Original entry on oeis.org

19, 37, 73, 109, 127, 163, 181, 271, 307, 433, 523, 541, 613, 631, 811, 1009, 1063, 1117, 1153, 1171, 1423, 1531, 1621, 1801, 2017, 2053, 2143, 2161, 2251, 2341, 2503, 2521, 3061, 3313, 3331, 3511, 4051, 4231, 5023, 5113, 6121, 6211, 6301, 8011, 8101

Offset: 1

Zak Seidov, May 16 2005

Subset of A061237 and A117674.

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1001..3000 from Vincenzo Librandi and Zak Seidov, terms 1..1000 from Vincenzo Librandi)

Cf. A000040 (primes), A007953 (sum of digits), A052224 (digit sum = 10).
Cf. A061237 (sum of digits == 1 (mod 9)).
Subsequence of A062340 (primes with digit sum divisible by 5).
Cf. A062339 (same for digit sum s = 4), A062341 (s = 5), A062343 (s = 8),  A106754 (s = 11), and others listed in A244918 (s = 68).

[p: p in PrimesUpTo(10000) | &+Intseq(p) eq 10]; // Vincenzo Librandi, Jul 08 2014

a:=proc(n) local nn: nn:=convert(n,base,10): if isprime(n)=true and add(nn[j], j=1..nops(nn))=10 then n else end if end proc: seq(a(n),n=1..10^4); # Emeric Deutsch, Mar 06 2008

Select[Prime[Range[100000]], Total[IntegerDigits[#]]==10 &] (* Vincenzo Librandi, Jul 08 2014 *)

forprime(p=19,8101,if(10==sumdigits(p),print(p","))) \\ Zak Seidov, Oct 08 2016

(A107579_nxt(p)=until(isprime(p=A228915(p)),); p); A107579_first(N=100)=vector(N, i, p=if(i>1, A107579_nxt(p), 19)) \\ M. F. Hasler, Mar 15 2022

from itertools import count, islice
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def agen(b=10, sod=10): # generator for any base, sum-of-digits
    if 0 <= sod < b:
        yield sod
    nzdigs = [i for i in range(1, b) if i <= sod]
    nzmultiset = []
    for d in range(1, b):
        nzmultiset += [d]*(sod//d)
    for d in count(2):
        fullmultiset = [0]*(d-1-(sod-1)//(b-1)) + nzmultiset
        for firstdig in nzdigs:
            target_sum, restmultiset = sod - int(firstdig), fullmultiset[:]
            restmultiset.remove(firstdig)
            for p in multiset_permutations(restmultiset, d-1):
                if sum(p) == target_sum:
                    t = int("".join(map(str, [firstdig]+p)), b)
                    if isprime(t):
                        yield t
                    if p[0] == target_sum:
                        break
print(list(islice(agen(), 45))) # Michael S. Branicky, Mar 10 2022

from sympy import isprime
def A107579(p=19):
    "Return a generator of the sequence of all primes >= p with the same digit sum as p."
    while True:
        if isprime(p): yield p
        p = A228915(p) # skip to next larger integer with the same digit sum
a=A107579(); [next(a) for  in range(50)] # _M. F. Hasler, Mar 16 2022

Intersection of A000040 (primes) and A052224 (digit sum = 10). - M. F. Hasler, Mar 09 2022

Edited by N. J. A. Sloane, Feb 20 2009 at the suggestion of Pacha Nambi

A138471 Number of numbers less than n having the same sum of digits.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0, 4, 4, 4, 4, 4, 4, 3, 2, 1, 0, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, 6, 6, 6, 6, 5, 4, 3, 2, 1, 0, 7, 7, 7, 6, 5, 4, 3, 2, 1, 0, 8, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 2, 3, 4, 5, 6

Offset: 0

Reinhard Zumkeller, Mar 19 2008

A138470(n) + a(n) + A138472(n) = n;
a(A051885(n)) = 0.
a(A228915(n)) = a(n)+1. - Robert Israel, May 26 2017

			a(42)=#{6,15,24,33}=4.

Robert Israel, Table of n, a(n) for n = 0..10000 (terms 0..1500 from Reinhard Zumkeller)
Index entries for Colombian or self numbers and related sequences

Cf. A007953, A051885, A138470, A138472, A228915.

N:= 1000: # to get a(0) to a(N)
C:= Vector(9*(1+ilog10(N))):
A[0]:= 0:
for n from 1 to N do
  s:= convert(convert(n,base,10),`+`);
  A[n]:= C[s];
  C[s]:= C[s]+1;
od:
seq(A[i],i=0..N); # Robert Israel, May 25 2017

Module[{nn=110,sd},sd=Total[IntegerDigits[#]]&/@Range[nn];Join[{0},Table[ Count[Take[sd,i-1],sd[[i]]],{i,nn}]]] (* Harvey P. Dale, Aug 14 2013 *)

a(n) = my(sdn=sumdigits(n)); sum(k=1, n-1, sumdigits(k) == sdn); \\ Michel Marcus, May 26 2017

A319021 Next larger integer with same sum of digits in base 3 as n.

Original entry on oeis.org

3, 4, 9, 6, 7, 10, 11, 14, 27, 12, 13, 18, 15, 16, 19, 20, 23, 28, 21, 22, 29, 24, 25, 32, 35, 44, 81, 30, 31, 36, 33, 34, 37, 38, 41, 54, 39, 40, 45, 42, 43, 46, 47, 50, 55, 48, 49, 56, 51, 52, 59, 62, 71, 82, 57, 58, 63, 60, 61, 64, 65, 68, 83, 66, 67, 72

Offset: 1

Rémy Sigrist, Sep 08 2018

This sequence is the base-3 variant of A057168 (base-2) and of A228915 (base-10).

All integers except those in A062318 appear in this sequence.

			The first terms, alongside the ternary representations of n and of a(n), are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   1     3      1     10
   2     4      2     11
   3     9     10    100
   4     6     11     20
   5     7     12     21
   6    10     20    101
   7    11     21    102
   8    14     22    112
   9    27    100   1000
  10    12    101    110
  11    13    102    111
  12    18    110    200
  13    15    111    120
  14    16    112    121
  15    19    120    201

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A053735, A057168, A062318, A228915.

nli3[n_]:=Module[{nd3=Total[IntegerDigits[n,3]],k=n+1},While[Total[IntegerDigits[k,3]]!=nd3,k++];k]; Array[nli3,70] (* Harvey P. Dale, Jun 27 2023 *)

a(n, base=3) = my (c=0); for (w=0, oo, my (d=n % base); if (d+1 < base && c, return ((n+1)*base^w + ((c-1)%(base-1) + 1)*base^((c-1)\(base-1))-1), c += d; n \= base))

def a(n, base=3):
    c, b, w = 0, base, 0
    while True:
        d = n%b
        if d+1 < b and c:
            return (n+1)*b**w + ((c-1)%(b-1)+1)*b**((c-1)//(b-1))-1
        c += d; n //= b; w += 1
print([a(n) for n in range(1, 67)]) # Michael S. Branicky, Jul 10 2022 after Rémy Sigrist

a(3^k) = 3^(k+1) for any k >= 0.

A053735(a(n)) = A053735(n).

A343604 a(n) is the least number > n with the same sum of balanced ternary digits as n.

Original entry on oeis.org

2, 3, 6, 7, 10, 15, 8, 9, 16, 11, 12, 19, 22, 31, 42, 17, 18, 23, 20, 21, 24, 25, 28, 43, 26, 27, 32, 29, 30, 33, 34, 37, 46, 35, 36, 49, 38, 39, 58, 67, 94, 123, 44, 45, 50, 47, 48, 51, 52, 55, 68, 53, 54, 59, 56, 57, 60, 61, 64, 69, 62, 63, 70, 65, 66, 73

Offset: 0

Rémy Sigrist, Apr 22 2021

This sequence can be extended to negative indexes by setting a(-n) = -A343605(n) for any n > 0.

			The first terms, in base 10 and in balanced ternary (where T denotes the digit -1), alongside A065363(n), are:
  n   a(n)  bter(n)  bter(a(n))  A065363(n)
  --  ----  -------  ----------  ----------
   0     2        0          1T           0
   1     3        1          10           1
   2     6       1T         1T0           0
   3     7       10         1T1           1
   4    10       11         101           2
   5    15      1TT        1TT0          -1
   6     8      1T0         10T           0
   7     9      1T1         100           1
   8    16      10T        1TT1           0
   9    11      100         11T           1
  10    12      101         110           2
  11    19      11T        1T01           1
  12    22      110        1T11           2

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Cf. A057168, A065363, A174658, A228915, A319021, A343605.

A065363(n) = { my (v=0, d); while (n, v+=d=centerlift(Mod(n,3)); n=(n-d)\3); v }
a(n) = my (s=A065363(n)); for (k=n+1, oo, if (s==A065363(k), return (k)))

a(9*n) = 9*n + 2.

a(A174658(n)) = A174658(n+1).

A375460 Lexicographically earliest sequence of distinct nonnegative terms arranged in successive chunks whose digitsum = 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 10, 11, 20, 6, 12, 100, 7, 21, 8, 101, 9, 1000, 13, 14, 10000, 15, 22, 16, 30, 17, 110, 18, 100000, 19, 23, 31, 1000000, 24, 40, 25, 102, 26, 200, 27, 10000000, 28, 32, 41, 33, 103, 34, 111, 35, 1001, 36, 100000000, 37, 42, 112, 43, 120, 44, 1010, 45, 1000000000

Offset: 1

Eric Angelini, Aug 15 2024

The first integer that will never appear in the sequence is 29, as its digitsum exceeds 10.
From Michael S. Branicky, Aug 16 2024: (Start)
Infinite since A052224 is infinite (as are all sequences with digital sum 1..10).
a(6492) has 1001 digits. (End)

			The first chunk of integers with digitsum 10 is (0,1,2,3,4);
the next one is (5,10,11,20),
the next one is (6,12,100),
the next one is (7,21),
the next one is (8,101),
the next one is (9,1000),
the next one is (13,14,10000), etc.
The concatenation of the above chunks produce the sequence.

Michael S. Branicky, Table of n, a(n) for n = 1..6491

Cf. A166311, A051885, A228915.

Numbers with digital sum 1..10: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10).

from itertools import islice
def bgen(ds): # generator of terms with digital sum ds
    def A051885(n): return ((n%9)+1)*10**(n//9)-1 # due to Chai Wah Wu
    def A228915(n): # due to M. F. Hasler
        p = r = 0
        while True:
            d = n % 10
            if d < 9 and r: return (n+1)*10**p + A051885(r-1)
            n //= 10; r += d; p += 1
    k = A051885(ds)
    while True: yield k; k = A228915(k)
def agen(): # generator of terms
    an, ds_block = 0, 0
    dsg = [None] + [bgen(i) for i in range(1, 11)]
    dsi = [None] + [(next(dsg[i]), i) for i in range(1, 11)]
    while True:
        yield an
        an, ds_an = min(dsi[j] for j in range(1, 11-ds_block))
        ds_block = (ds_block + ds_an)%10
        dsi[ds_an] = (next(dsg[ds_an]), ds_an)
print(list(islice(agen(), 61))) # Michael S. Branicky, Aug 16 2024

a(46) and beyond from Michael S. Branicky, Aug 16 2024.

A375967 a(n) is the least number > n with the same digit average as n.

Original entry on oeis.org

11, 13, 15, 17, 19, 39, 59, 79, 99, 1001, 20, 21, 22, 23, 24, 25, 26, 27, 28, 102, 30, 31, 32, 33, 34, 35, 36, 37, 38, 1005, 40, 41, 42, 43, 44, 45, 46, 47, 48, 105, 50, 51, 52, 53, 54, 55, 56, 57, 58, 1009, 60, 61, 62, 63, 64, 65, 66, 67, 68, 108, 70, 71, 72

Offset: 1

Rémy Sigrist, Sep 04 2024

The digit average of a number n is its sum of digits divided by its number of digits: A007953(n) / A055642(n).

			The first terms, alongside the corresponding digit average, are:
  n   a(n)  Digit average
  --  ----  -------------
   1    11              1
   2    13              2
   3    15              3
   4    17              4
   5    19              5
   6    39              6
   7    59              7
   8    79              8
   9    99              9
  10  1001            1/2
  11    20              1
  12    21            3/2

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A007953, A055642, A228915, A375968.

a[n_]:=Module[{k=0}, While[k<=n || Mean[IntegerDigits[k]] != Mean[IntegerDigits[n]], k++]; k]; Array[a,63] (* Stefano Spezia, Sep 07 2024 *)

avg(n, base) = my (d = digits(n, base)); vecsum(d) / max(1, #d)
a(n, base = 10) = { my (v = avg(n, base)); for (m = n+1, oo, if (avg(m, base)==v, return (m););); }

PARI
```
\\ See Links section.
```

A287076 a(n) = least k > n with the same sum of digits as n in some base b > 1.

Original entry on oeis.org

2, 4, 5, 6, 6, 9, 10, 12, 10, 12, 13, 16, 14, 16, 19, 20, 18, 20, 21, 22, 22, 24, 25, 30, 26, 28, 29, 30, 30, 36, 33, 34, 34, 36, 37, 40, 38, 40, 42, 42, 42, 44, 45, 48, 46, 48, 49, 56, 50, 52, 53, 56, 54, 57, 57, 58, 58, 60, 61, 64, 62, 66, 67, 66, 66, 68, 69

Offset: 1

Rémy Sigrist, May 19 2017

More formally: a(n) = Min_{b>1} f_b(n), where f_b(n) = least k > n with the same sum of digits as n in base b.
We have the following properties:
- f_b(b) = b^2 for any b > 1,
- f_b(b^k) = b^(k+1) for any b > 1 and k >= 0,
- f_b(n) = b + n - 1 for any b > 1 and n < b,
- f_b(n) - n >= b - 1 for any b > 1 and n > 0.
Also, f_2 = A057168 and f_10 = A228915.
For any n > 0, n < a(n) <= 2*n.
Conjecturally, a(n) ~ n.
The derived sequence e(n) = a(n) - n is unbounded: for any n > 0:
- for any b such that 1 < b <= n, let x_b = the least power of b such that f_b(i*x_b) - i*x_b >= n for any i > 0,
- let X = Lcm_{b=2..n} x_b,
- then f_b(X) - X >= n for any b such that 1 < b <= n,
- also, f_b(X) - X >= b - 1 >= n for any b > n,
- hence a(X) - X = e(X) >= n, QED.

			The following table shows f_b(8) for all bases b > 1:
b    f_b(8)   8 in base b   f_b(8) in base b
--   ------   -----------   ----------------
2        16        "1000"            "10000"
3        14          "22"              "112"
4        17          "20"              "101"
5        12          "13"               "22"
6        13          "12"               "21"
7        14          "11"               "20"
8        64          "10"              "100"
b>8     b+7           "8"               "17"
Hence, a(8) = f_5(8) = 12.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A287076

Cf. A057168, A228915.

A375387 a(n) is the least number k whose sum of digits in base 10 is n and that is palindromic in base n, or -1 if no such number exists.

Original entry on oeis.org

-1, 130, 41, 123, 16, 170, -1, 55, 155, 39, 274, 239, 96, 187, 494, 2925, 685, 1784, 1389, 859, 599, 1779, 1978, 989, 6597, 5887, 6968, 8499, 5989, 17969, 29859, 17899, 28898, 435897, 38989, 2089469, 1788960, 498847, 2886278, 487878, 919996, 4098689, 898794, 1896967

Offset: 3

Jean-Marc Rebert, Aug 13 2024

A positive integer that is a multiple of 3 ends with 0 in base 3, so it cannot be a palindrome in base 3.
A positive integer that is a multiple of 9 ends with 0 in base 9, so it cannot be a palindrome in base 9.
From Michael S. Branicky, Aug 15 2024: (Start)
Regarding a(2): To be a palindrome in base 2, it must end with 1, hence odd. To be odd and have digit sum 2 in base 10, it must be of the form t_d = 10^(d-1) + 1, d > 1 (a d-digit base-10 number).  t_d is not divisible by 3, and base-2 palindromes with even length (i.e., number of binary digits) are divisible by 3, so, if a(2) exists, it must be a base-2 palindrome with odd length.
Computer search shows no such terms with d <= 10^6, so a(2), if it exists, has > 10^6 decimal digits. (End)

			a(5) = 41, because 4 + 1 = 5 and 41 = 131_5, and no lesser number has this property.
First terms are:
  130 = 2002_4
  41  = 131_5
  123 = 3323_6
  16  = 22_7
  170 = 252_8

Michael S. Branicky, Table of n, a(n) for n = 3..149
Michael S. Branicky, Python programs for OEIS A375387
Jean-Marc Rebert, a375387_1e10

Cf. A002113, A007953, A051885, A065531, A107129, A228915, A253594.

isok(k, n) = if (sumdigits(k)==n, my(d=digits(k, n)); d==Vecrev(d));
a(n) = if ((n==3) || (n==9), return((-1))); my(k=1); while (!isok(k,n), k++); k; \\ Michel Marcus, Aug 13 2024

# see Links for faster variants
from itertools import count
from sympy.ntheory import is_palindromic
def a(n):
    if n in {3, 9}: return -1
    return next(k for k in count(10**(n//9)-1) if sum(map(int, str(k)))==n and is_palindromic(k, n))
print([a(n) for n in range(3, 47)]) # Michael S. Branicky, Aug 13 2024

A375477 Lexicographically earliest sequence of distinct nonnegative terms arranged in successive chunks whose digitsum = 10, said chunks being "linked" (see the Comments section for an explanation).

Original entry on oeis.org

0, 1, 2, 3, 4, 40, 6, 60, 10, 12, 20, 5, 21, 11, 8, 80, 101, 13, 15, 50, 14, 41, 23, 30, 7, 70, 100, 1001, 16, 102, 22, 24, 42, 31, 17, 10001, 19, 91, 103, 33, 32, 104, 43, 111, 105, 110, 100001, 106, 201, 107, 1000001, 109, 901, 112, 51, 113, 120, 10000001, 114, 121

Offset: 1

Eric Angelini and Michael S. Branicky, Aug 17 2024

The 1st chunk with digitsum = 10 is (0, 1, 2, 3, 4), ending with a "4". The next chunk with digitsum = 10 must start with a "4" (this is the "link") and is thus (40, 6). As the next chunk with digitsum = 10 must start with a "6", we have (60, 10, 12). The next chunk with digitsum = 10 must start with a "2" and we have (20, 5, 21), etc.
No chunk is allowed to end with a zero.  Thus, no intermediate chunk digit sum can be 9, and anytime a chunk needs a digitsum of 2 to "complete", the next term must be of the form 10^k + 1 for k >= 1.
Infinite since there are an infinity of terms with digits sums <= 10.
a(5367) has 1001 digits.

Michael S. Branicky, Table of n, a(n) for n = 1..5366
Eric Angelini, Tile my sequence, personal blog of the author.

Cf. A375460.

from itertools import count, islice
def bgen(ds): # generator of terms with digital sum ds
    def A051885(n): return ((n%9)+1)*10**(n//9)-1 # due to Chai Wah Wu
    def A228915(n): # due to M. F. Hasler
        p = r = 0
        while True:
            d = n % 10
            if d < 9 and r: return (n+1)*10**p + A051885(r-1)
            n //= 10; r += d; p += 1
    k = A051885(ds)
    while True: yield k; k = A228915(k)
def agen(): # generator of terms
    an, ds_block, seen, link_set, min2 = 0, 0, set(), "123456789", 11
    while True:
        yield an
        seen.add(an)
        if ds_block == 8:
            while min2 in seen: min2 = 10*min2 - 9
            an, ds_an, link_an = min2, 2, "1"
        else:
            cand_ds = list(range(1, 9-ds_block)) + [10-ds_block]
            dsg = [0] + [bgen(i) for i in range(1, 11-ds_block)]
            dsi = [0] + [(next(dsg[i]), i) for i in range(1, 11-ds_block)]
            while True:
                k, ds_k = min(dsi[j] for j in cand_ds)
                if k not in seen:
                    sk, dst = str(k), ds_k + ds_block
                    if sk[0] in link_set:
                        if dst < 9 or (dst == 10 and k%10 != 0):
                            an, ds_an, link_an = k, ds_k, sk[-1]
                            break
                dsi[ds_k] = (next(dsg[ds_k]), ds_k)
        ds_block = ds_block + ds_an
        if ds_block == 10: ds_block, link_set = 0, link_an
        else: link_set = "123456789"
print(list(islice(agen(), 60)))

cp's OEIS Frontend

A052224 Numbers whose sum of digits is 10.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

PARI

Python

Python

Formula

Extensions

A107579 Primes with digit sum 10.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

PARI

Python

Python

Formula

Extensions

A138471 Number of numbers less than n having the same sum of digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A319021 Next larger integer with same sum of digits in base 3 as n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A343604 a(n) is the least number > n with the same sum of balanced ternary digits as n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A375460 Lexicographically earliest sequence of distinct nonnegative terms arranged in successive chunks whose digitsum = 10.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs