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A344633
Lengths k of k-digit integers of the form 1, 12, 123, 1234, ... (A057137) which are divisible by k.
0
1, 2, 3, 5, 6, 9, 10, 12, 14, 15, 16, 18, 30, 90, 96, 110, 197, 210, 270, 330, 390, 410, 630, 810, 930, 959, 990, 1110, 1170, 1210, 1230, 1470, 1710, 1890, 1956, 2310, 2430, 2530, 2538, 2710, 2730, 2790, 2802, 2922, 2970, 3330, 3510, 3519, 3630, 3690, 4115, 4245
OFFSET
1,2
COMMENTS
It is easy to prove that 10*3^k, k >= 0 is always a solution.
FORMULA
{n: n|A057137(n)}. - R. J. Mathar, Aug 16 2021
EXAMPLE
3 is a term since 123 is divisible by 3 (123 = 3*41).
MAPLE
for n from 1 to 5000 do
if modp(A057137(n), n) = 0 then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Aug 16 2021
PROG
(Python)
a ="1234567890"
for k in range(10):
a = a + a
sol = ""
for n in range(1, len(a)):
if int(a[0:n]) % n == 0:
sol = sol + str(n) + ", "
print(sol)
(PARI) f(n) = 137174210*10^n\1111111111; \\ A057137
isok(k) = (f(k) % k) == 0; \\ Michel Marcus, Aug 16 2021
CROSSREFS
Cf. A057137.
Sequence in context: A188375 A047331 A288480 * A029451 A029455 A234718
KEYWORD
nonn,base
AUTHOR
Reiner Moewald, May 26 2021
STATUS
approved