A369702 Smallest k > n such that the decimal expansion of k*n contains n as a substring of consecutive decimal digits.

10, 6, 10, 6, 7, 10, 10, 10, 10, 11, 100, 26, 87, 51, 21, 26, 69, 51, 63, 21, 58, 51, 97, 26, 29, 51, 100, 46, 79, 31, 100, 51, 100, 51, 41, 38, 100, 51, 87, 41, 59, 51, 100, 51, 61, 51, 74, 51, 51, 51, 69, 76, 100, 100, 61, 76, 100, 79, 61, 61, 92, 100, 100, 76, 81, 100, 100, 76, 97, 71

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Formula

a(n) <= 10^A055642(n). - Michael S. Branicky, Jan 29 2024

Example

a(12) = 26 because 26 is the smallest integer greater than 12 such that 12 * 26 = 312 contains 12 as a substring.

Mathematica

a[n_]:=(k=n+1; While[!StringContainsQ[ToString[n*k], ToString@n], k++]; k); Array[a, 70]

Prog

(Python)
from itertools import count
def a(n):
    s = str(n)
    return next(k for k in count(n+1) if s in str(k*n))
print([a(n) for n in range(1, 71)]) # Michael S. Branicky, Jan 29 2024

Crossrefs

Cf. A055642.

Sequence in context: A072930 A071358 A167873 * A033986 A049004 A104645

Adjacent sequences: A369699 A369700 A369701 * A369703 A369704 A369705

Keyword

nonn,base,look

Author

Giorgos Kalogeropoulos, Jan 29 2024

Status

approved