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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
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
Sequence in context: A043862 A043871 A269987 * A130694 A269748 A153831
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.)