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A014836
Sum modulo n of all the digits of n in every base from 2 to n-1.
6
2, 3, 2, 3, 1, 0, 2, 4, 1, 9, 6, 9, 14, 9, 5, 0, 14, 11, 19, 3, 20, 7, 18, 25, 5, 2, 24, 12, 5, 28, 9, 18, 0, 8, 0, 10, 26, 12, 3, 30, 21, 19, 24, 37, 27, 39, 17, 14, 36, 35, 24, 3, 32, 17, 42, 1, 47, 56, 44, 0, 11, 50, 21, 2, 55, 55, 17, 5, 61, 69, 55, 3, 14, 14, 59, 38, 22, 62
OFFSET
3,1
LINKS
FORMULA
a(n) = A014837(n) mod n. - R. J. Mathar, Aug 10 2008
MATHEMATICA
Table[ Mod[Plus@@Table[Plus@@IntegerDigits[n, k], {k, 2, n-1}], n], {n, 3, 100}]
PROG
(Python)
from sympy.ntheory import digits
def A014836(n):
c = 0
for b in range(2, n):
for d in digits(n, b)[1:]:
c = (c+d)%n
return c # Chai Wah Wu, Oct 28 2025
(PARI) a(n) = sum(b=2, n-1, sumdigits(n, b)) % n; \\ Michel Marcus, Oct 29 2025
CROSSREFS
KEYWORD
nonn,base
STATUS
approved