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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
OFFSET
1,1
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
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Jan 09 2001
STATUS
approved