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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.
14
13, 17, 29, 16, 27, 30, 42, 46, 62, 68, 86, 92, 114, 122, 147, 154, 182, 192, 222, 232, 266, 278, 314, 326, 367, 380, 422, 436, 482, 498, 546, 562, 614, 632, 688, 704, 762, 782, 842, 862, 926, 948, 1014, 1036, 1107, 1130, 1202, 1226, 1302, 1328, 1406, 1432
OFFSET
2,1
LINKS
EXAMPLE
a(10) = 62, from A003635.
MATHEMATICA
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} ]
PROG
(Python)
from itertools import count, combinations_with_replacement
from sympy.ntheory import digits
def A052491(n):
for k in count(1):
for l in count(1):
if (n-1)*l*k < n**(l-1):
return k
for d in combinations_with_replacement(range(n), l):
if (s:=sum(d)) > 0 and sorted(digits(s*k, n)[1:]) == list(d):
break
else:
continue
break # Chai Wah Wu, May 09 2023
CROSSREFS
KEYWORD
nonn,nice,easy,base
AUTHOR
J. H. Conway, Dec 30 2000
EXTENSIONS
Corrected and extended by David Radcliffe, Jan 08 2001
More terms from David W. Wilson, Jan 10 2001
STATUS
approved