A052223 -id:A052223 - cp's OEIS frontend

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

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.

A121476 Palindromes with digit sum 9.

Original entry on oeis.org

9, 171, 252, 333, 414, 10701, 11511, 12321, 13131, 20502, 21312, 22122, 30303, 31113, 40104, 1007001, 1015101, 1023201, 1031301, 1105011, 1113111, 1121211, 1203021, 1211121, 1301031, 2005002, 2013102, 2021202, 2103012, 2111112, 2201022, 3003003, 3011103

Offset: 1

Lekraj Beedassy, Aug 01 2006

Intersection of A002113 and A052223.

Cf. A121477.

Select[Range[3100000],PalindromeQ[#]&&Total[IntegerDigits[#]]==9&] (* James C. McMahon, Oct 19 2024 *)

Missing 1301031 and more terms terms from Sean A. Irvine, Jun 04 2024

A279771 Numbers n such that the sum of digits of 11n equals 11.

Original entry on oeis.org

19, 28, 37, 46, 55, 64, 73, 82, 190, 280, 370, 460, 550, 640, 730, 820, 919, 928, 937, 946, 955, 964, 973, 982, 991, 1819, 1828, 1837, 1846, 1855, 1864, 1873, 1882, 1891, 1900, 2728, 2737, 2746, 2755, 2764, 2773, 2782, 2791, 2800, 3637, 3646, 3655, 3664

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088404 = A069537/2 through A088410 = A069543/8.

Cf. A007953 (digital sum), Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).

Select[Range@ 3664, Total@IntegerDigits[11 #] == 11 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(11*n)==11
```

A333814 Multiples of 12 whose sum of digits is 12.

Original entry on oeis.org

48, 84, 156, 192, 228, 264, 336, 372, 408, 444, 480, 516, 552, 624, 660, 732, 804, 840, 912, 1056, 1092, 1128, 1164, 1236, 1272, 1308, 1344, 1380, 1416, 1452, 1524, 1560, 1632, 1704, 1740, 1812, 1920, 2028, 2064, 2136, 2172, 2208, 2244, 2280, 2316, 2352, 2424

Offset: 1

Bernard Schott, Apr 06 2020

If m is a term, 10*m is also a term.

			732 = 12 * 61 and 7 + 3 + 2 = 12, hence 732 is a term.

Intersection of A235151 (sum of digits = 12) and A008594 (multiples of 12).
Multiples of k whose sum of digits = k: A011557 (k=1), A069537 (k=2), A052217 (k=3), A063997 (k=4), A069540 (k=5), A062768 (k=6), A063416 (k=7), A069543 (k=8), A052223 (k=9), A333834 (k=10), A283742 (k=11), this sequence (k=12), A283737 (k=13).
Cf. A008594 (multiples of 12), A235151 (sum of digits = 12).
Cf. A057147 (a(n) = n times sum of digits of n).

Select[12 * Range[200], Plus @@ IntegerDigits[#] == 12 &] (* Amiram Eldar, Apr 06 2020 *)

is(n)=sumdigits(n)==12 && n%4==0 \\ Charles R Greathouse IV, Apr 07 2020

a(n) ~ A235151(n). - Charles R Greathouse IV, Apr 07 2020

A333834 Multiples of 10 whose sum of digits is 10.

Original entry on oeis.org

190, 280, 370, 460, 550, 640, 730, 820, 910, 1090, 1180, 1270, 1360, 1450, 1540, 1630, 1720, 1810, 1900, 2080, 2170, 2260, 2350, 2440, 2530, 2620, 2710, 2800, 3070, 3160, 3250, 3340, 3430, 3520, 3610, 3700, 4060, 4150, 4240, 4330, 4420, 4510

Offset: 1

Bernard Schott, Apr 07 2020

If m is a term, 10*m is also a term.

Intersection of A052224 (sum of digits = 10) and A008592 (multiples of 10).

			2440 = 10 * 244 and 2 + 4 + 4 + 0 = 10, hence 2440 is a term.

Multiples of k whose sum of digits = k: A011557 (k=1), A069537 (k=2), A052217 (k=3), A063997 (k=4), A069540 (k=5), A062768 (k=6), A063416 (k=7), A069543 (k=8), A052223 (k=9), this sequence (k=10), A283742 (k=11), A333814 (k=12), A283737 (k=13).
Subsequence of A218292.
Cf. A008592 (multiples of 10), A052224 (sum of digits = 10).
Cf. A057147 (a(n) = n times sum of digits of n)

Select[10 * Range[500], Plus @@ IntegerDigits[#] == 10 &] (* Amiram Eldar, Apr 07 2020 *)

a(n) = 10*A052224(n). - Charles R Greathouse IV, Apr 07 2020

A375824 Triangular numbers whose sum of digits is 9.

Original entry on oeis.org

36, 45, 153, 171, 351, 630, 1035, 1431, 2016, 3240, 3321, 4005, 8001, 10440, 13041, 13203, 16110, 21321, 23220, 25200, 101025, 105111, 114003, 222111, 320400, 321201, 1010331, 1241100, 1313010, 1400301, 2013021, 2031120, 2410110, 4020030, 10006101, 11203011, 20012301, 32004000, 32012001, 33020001

Offset: 1

Robert Israel, Aug 30 2024

Infinite subsequences include 2 * 10^(2*k) + 13 * 10^k + 21, 2 * 10^(2*k) + 31 * 10^k + 120, 32 * 10^(2*k) + 4 * 10^k, and 32 * 10^(2*k) + 12 * 10^k + 1.

Conjecture: the last term not of one of those subsequences is a(53) = 210010000005.

			a(4) = 153 is a term because 153 = 17 * 18/2 is a triangular number and 1 + 5 + 3 = 9.

Robert Israel, Table of n, a(n) for n = 1..95

Intersection of A000217 and A052223. Contained in A117404 and A076713.

F:= proc(d,s) option remember;
# d-digit numbers with sum of digits s
      local R,i;
      R:= {};
      for i from 0 to min(s,9) do
        R:= R union map(t -> 10*t+i, procname(d-1,s-i))
      od;
      R
end proc:
F(1,0):= {}:
for i from 1 to 9 do F(1,i):= {i} od:
sort(convert(`union`(seq(select(t -> issqr(1+8*t), F(d,9)),d=1..12)),list));

Select[Range[10000](Range[10000]+1)/2,DigitSum[#]==9 &] (* Stefano Spezia, Sep 01 2024 *)

select(x->(sumdigits(x)==9), vector(10000, n, n*(n+1)/2)) \\ Michel Marcus, Aug 31 2024

cp's OEIS Frontend

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

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A121476 Palindromes with digit sum 9.

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A279771 Numbers n such that the sum of digits of 11n equals 11.

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A333814 Multiples of 12 whose sum of digits is 12.

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A333834 Multiples of 10 whose sum of digits is 10.

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A375824 Triangular numbers whose sum of digits is 9.

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