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A052491 Smallest "inconsummate number" in base n: smallest number such that in base n, no number is this multiple of the sum of its digits.

%I A052491 #31 May 10 2023 10:43:36
%S A052491 13,17,29,16,27,30,42,46,62,68,86,92,114,122,147,154,182,192,222,232,
%T A052491 266,278,314,326,367,380,422,436,482,498,546,562,614,632,688,704,762,
%U A052491 782,842,862,926,948,1014,1036,1107,1130,1202,1226,1302,1328,1406,1432
%N A052491 Smallest "inconsummate number" in base n: smallest number such that in base n, no number is this multiple of the sum of its digits.
%H A052491 Chai Wah Wu, <a href="/A052491/b052491.txt">Table of n, a(n) for n = 2..174</a>
%e A052491 a(10) = 62, from A003635.
%t A052491 Do[n = 1; While[k = n; While[ Apply[ Plus, IntegerDigits[k, b] ]*n != k && k < 100n, k += n ]; k != 100n, n++ ]; Print[n], {b, 2, 54} ]
%o A052491 (Python)
%o A052491 from itertools import count, combinations_with_replacement
%o A052491 from sympy.ntheory import digits
%o A052491 def A052491(n):
%o A052491     for k in count(1):
%o A052491         for l in count(1):
%o A052491             if (n-1)*l*k < n**(l-1):
%o A052491                 return k
%o A052491             for d in combinations_with_replacement(range(n),l):
%o A052491                 if (s:=sum(d)) > 0 and sorted(digits(s*k,n)[1:]) == list(d):
%o A052491                     break
%o A052491             else:
%o A052491                 continue
%o A052491             break # _Chai Wah Wu_, May 09 2023
%Y A052491 Cf. A003635, A058898-A058907.
%K A052491 nonn,nice,easy,base
%O A052491 2,1
%A A052491 _J. H. Conway_, Dec 30 2000
%E A052491 Corrected and extended by _David Radcliffe_, Jan 08 2001
%E A052491 More terms from _David W. Wilson_, Jan 10 2001