A003635 Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10). (Formerly M5325)

62, 63, 65, 75, 84, 95, 161, 173, 195, 216, 261, 266, 272, 276, 326, 371, 372, 377, 381, 383, 386, 387, 395, 411, 416, 422, 426, 431, 432, 438, 441, 443, 461, 466, 471, 476, 482, 483, 486, 488, 491, 492, 493, 494, 497, 498, 516, 521, 522, 527, 531, 533, 536

Offset

1,1

References

J. H. Conway, personal communication.

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

Links

Daniel Mondot, Table of n, a(n) for n = 1..10867

Maple

For Maple code see A058906.

Mathematica

nmax = 1000; Reap[ Do[k = n; kmax = 100*n; While[ Tr[ IntegerDigits[k]]*n != k && k < kmax, k = k + n]; If[k == kmax, Sow[n]], {n, 1, nmax}]][[2, 1]] (* Jean-François Alcover, Jul 12 2012 *)

Prog

(Python)
from itertools import count, islice, combinations_with_replacement
def A003635_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue, 1)):
        for l in count(1):
            if 9*l*n < 10**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(10), l):
                if (s:=sum(d))>0 and sorted(str(s*n)) == [str(e) for e in d]:
                    break
            else:
                continue
            break
A003635_list = list(islice(A003635_gen(), 20)) # Chai Wah Wu, May 09 2023

Crossrefs

Cf. A003634, A052489, A052490, A052491, A058898-A058917.

Sequence in context: A033382 A143733 A296766 * A188631 A076764 A367090

Adjacent sequences: A003632 A003633 A003634 * A003636 A003637 A003638

Keyword

nonn,easy,nice,base

Author

N. J. A. Sloane and Mira Bernstein

Status

approved