A003634 Smallest positive integer that is n times its digit sum, or 0 if no such number exists. (Formerly M5054)

1, 18, 27, 12, 45, 54, 21, 72, 81, 10, 198, 108, 117, 126, 135, 144, 153, 162, 114, 180, 378, 132, 207, 216, 150, 234, 243, 112, 261, 270, 372, 576, 594, 102, 315, 324, 111, 342, 351, 120, 738, 756, 516, 792, 405, 230, 423, 432, 441, 450, 918, 312, 954, 972

Offset

1,2

Comments

a(n) = 0 for n = 62, 63, 65, ... (A003635). - Robert G. Wilson v, Aug 15 2000

References

J. H. Conway, personal communication.

Anthony Gardiner, Mathematical Puzzling, Dover Publications, Inc., Mineola, NY, 1987, Page 11.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Example

a(3) = 27 because no number less than 27 has a digit sum equal to 3 times the number.

Mathematica

Do[k = n; While[Apply[Plus, RealDigits[k][[1]]]*n != k, k += n]; Print[k], {n, 1, 61}]
With[{ll=Select[Table[{n, n/Total[IntegerDigits[n]]}, {n, 1000}], IntegerQ[ #[[2]]]&]}, Table[Select[ll, #[[2]]==i&, 1][[1, 1]], {i, 60}]] (* Harvey P. Dale, Mar 09 2012 *)

Prog

(Python)
def sd(n): return sum(map(int, str(n)))
def a(n):
  m = 1
  while m != n*sd(m): m += 1
  return m
print([a(n) for n in range(1, 62)]) # Michael S. Branicky, Jan 18 2021
(Python)
from itertools import count, combinations_with_replacement
def A003634(n):
    for l in count(1):
        if 9*l*n < 10**(l-1): return 0
        c = 10**l
        for d in combinations_with_replacement(range(10), l):
            if sorted(str(a:=sum(d)*n)) == [str(e) for e in d] and a>0:
                c = min(c, a)
        if c < 10**l:
            return c # Chai Wah Wu, May 09 2023

Crossrefs

Cf. A005349, A003635.

Sequence in context: A337523 A167336 A328687 * A338383 A338385 A220100

Adjacent sequences: A003631 A003632 A003633 * A003635 A003636 A003637

Keyword

nonn,base,easy,look,nice

Author

N. J. A. Sloane, Mira Bernstein

Status

approved