A344633 Length k of k-digit integers of the form 1, 12, 123, 1234, ... (A057137) which are divisible by k.

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.

Links

Table of n, a(n) for n=1..52.

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

Adjacent sequences: A344630 A344631 A344632 * A344634 A344635 A344636

Keyword

nonn,base

Author

Reiner Moewald, May 26 2021

Status

approved