A052221 -id:A052221 - cp's OEIS frontend

A069526 Smallest multiple of n with digit sum = 7, or 0 if no such number exists, e.g. a(3k)= a(11k) = 0.

7, 16, 0, 16, 25, 0, 7, 16, 0, 70, 0, 0, 52, 70, 0, 16, 34, 0, 133, 160, 0, 0, 115, 0, 25, 52, 0, 700, 232, 0, 124, 160, 0, 34, 70, 0, 0, 304, 0, 160, 205, 0, 43, 0, 0, 322, 1222, 0, 2401, 250, 0, 52, 106, 0, 0, 7000, 0, 232, 4012, 0, 61, 124, 0, 1024, 520, 0, 11122, 340

Offset: 1

Amarnath Murthy, Apr 01 2002

Either no multiples of 37 have digit sum 7 or their first values are > 10000000. - Larry Reeves (larryr(AT)acm.org), Jul 02 2002

No multiples of 3, 11, 37, 101 or 271 have digit sum 7. - Robert Israel, Feb 13 2024

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A052221, A069521, A069522, A069523, A069524, A069525, A069527, A069528.

unfinished:= true: V:= Vector(300): V0:= select(t -> igcd(t, 3*11*37*101*271) = 1, {$1..300}):
for i1 from 0 while unfinished do
  for i2 from 0 to i1 while unfinished do
    for i3 from 0 to i2 while unfinished do
      for i4 from 0 to i3 while unfinished do
        for i5 from 0 to i4 while unfinished do
          for i6 from 0 to i5 while unfinished do
            for i7 from 0 to i6 while unfinished do
              v:= 10^i1 + 10^i2 + 10^i3 + 10^i4 + 10^i5 + 10^i6 + 10^i7;
              dv:= numtheory:-divisors(v);
              for s in V0 intersect dv do
                V[s]:= v;
              od;
              V0:= V0 minus dv;
              unfinished:= evalb(V0 <> {});
od od od od od od od:
convert(V,list); # Robert Israel, Feb 13 2024

a(n)= n*A088396(n). - R. J. Mathar, Aug 06 2019

More terms from Larry Reeves, Jul 02 2002

A119461 Zero-free numbers with digit sum equal to 7.

Original entry on oeis.org

7, 16, 25, 34, 43, 52, 61, 115, 124, 133, 142, 151, 214, 223, 232, 241, 313, 322, 331, 412, 421, 511, 1114, 1123, 1132, 1141, 1213, 1222, 1231, 1312, 1321, 1411, 2113, 2122, 2131, 2212, 2221, 2311, 3112, 3121, 3211, 4111, 11113, 11122, 11131, 11212, 11221, 11311, 12112, 12121, 12211, 13111, 21112, 21121, 21211, 22111, 31111, 111112, 111121, 111211, 112111, 121111, 211111, 1111111

Offset: 1

Zak Seidov, May 20 2006

There are exactly 64 such numbers while numbers with digit sum equal to 7 (A052221) are infinite.

Subsequence of A052221.

Union[Flatten[Table[FromDigits/@Select[Tuples[Range[7],n],Total[#]==7&],{n,7}]]] (* Harvey P. Dale, Aug 29 2015 *)

def ok(n): s = str(n); return '0' not in s and sum(map(int, s)) == 7
print(list(filter(ok, range(1111112)))) # Michael S. Branicky, Jul 16 2021

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.

A118703 Zero-free primes with digit sum equal to 7.

Original entry on oeis.org

7, 43, 61, 151, 223, 241, 313, 331, 421, 1123, 1213, 1231, 1321, 2113, 2131, 2221, 2311, 3121, 4111, 11113, 11131, 11311, 12211, 21121, 21211, 22111, 111121, 111211, 112111

Offset: 1

Zak Seidov, May 20 2006

There are exactly 29 such primes the largest one being 112111.

Cf. A062337, A052221, A119461.

Select[Prime[Range[11000]],DigitCount[#,10,0]==0&&Total[ IntegerDigits[ #]] == 7&] (* Harvey P. Dale, Dec 04 2020 *)

isok(n) = isprime(n) && (sumdigits(n) == 7) && (vecmin(digits(n)) != 0); \\ Michel Marcus, Oct 10 2013

A259144 Number of n-digit primes whose sum of digits is 7.

Original entry on oeis.org

1, 2, 7, 20, 28, 58, 95, 154, 226, 278, 403, 570, 734, 949, 1200, 1515, 1931, 2328, 2908, 3529, 4196, 5034, 5800, 6870, 7871, 9132, 10574, 12359, 14005, 15871, 17924, 20231, 22505, 25903, 28800, 31532, 34830, 38479, 43334, 48847, 52769, 57173, 61545, 67774, 75186

Offset: 1

Zak Seidov, Jun 19 2015

Giovanni Resta, Table of n, a(n) for n = 1..100

Cf. A007953, A052221, A062337.

a(n)=n--; my(A,B,C,D); sum(a=0,n, A=10^n+10^a+1; sum(b=a,n, B=A+10^b; sum(c=b,n, C=B+10^c; sum(d=c,n, D=C+10^d; sum(e=d,n, isprime(D+10^e)))))) \\ Charles R Greathouse IV, Jun 19 2015

More terms from Alois P. Heinz, Jun 19 2015

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
```

cp's OEIS Frontend

A069526 Smallest multiple of n with digit sum = 7, or 0 if no such number exists, e.g. a(3k)= a(11k) = 0.

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A119461 Zero-free numbers with digit sum equal to 7.

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

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A118703 Zero-free primes with digit sum equal to 7.

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A259144 Number of n-digit primes whose sum of digits is 7.

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

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