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 A058906 Inconsummate numbers in base 11: no number is this multiple of the sum of its digits (in base 11). 10
 68, 70, 79, 80, 82, 92, 104, 200, 202, 212, 214, 224, 225, 248, 260, 314, 320, 332, 380, 392, 452, 458, 464, 490, 502, 508, 512, 513, 514, 518, 520, 524, 530, 562, 568, 574, 578, 579, 580, 584, 585, 590, 592, 595, 598, 599, 622, 628, 634, 635 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..50. MAPLE digitsum := proc (n, b) local i; add(i, i=convert(n, base, b)) end; b := 11:N := 43922; L := []: for n from 1 to N do k := digitsum(n, b): if (n mod k)=0 then L := [op(L), n/k] fi: od: M := []: for i from 1 to 1000 do if not(member(i, L)) then M := [op(M), i] fi od: lprint(M); MATHEMATICA base = 11; Do[k = n; While[ Apply[ Plus, IntegerDigits[k, base] ]*n != k && k < 250n, k += n]; If[k == 250n, Print[n] ], {n, 1, 10^3} ] PROG (Python) from itertools import count, islice, combinations_with_replacement from sympy.ntheory import digits def A058906_gen(startvalue=1): # generator of terms >= startvalue for n in count(max(startvalue, 1)): for l in count(1): if 10*l*n < 11**(l-1): yield n break for d in combinations_with_replacement(range(11), l): if (s:=sum(d)) > 0 and sorted(digits(s*n, 11)[1:]) == list(d): break else: continue break A058906_list = list(islice(A058906_gen(), 20)) # Chai Wah Wu, May 09 2023 CROSSREFS Cf. A003635, A052491, A058898-A058907. Sequence in context: A043862 A043871 A269987 * A130694 A269748 A153831 Adjacent sequences: A058903 A058904 A058905 * A058907 A058908 A058909 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Jan 09 2001 STATUS approved

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Last modified June 24 10:07 EDT 2024. Contains 373674 sequences. (Running on oeis4.)