OFFSET
1,1
COMMENTS
a(n) is 0 when n is divisible by 10, but when a(n) = 0, n is not always divisible by 10. For example, for n = 625, 1875, 3125, 4375, ... a(n) = 0 because no such k has been found yet for these numbers.
Conjecture: a(n) > 0 for all n that are not divisible by 5.
a(625*k) = 0 for k > 0 as the last four digits of (625*k), i.e., (625*k) mod 10000 always contains a nonprime digit. - David A. Corneth, Apr 21 2021
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 56479
EXAMPLE
a(4) = 8 because 8 is the smallest number k such that 8*4 = 32 contains only prime digits.
PROG
(PARI) a(n) = if ((n % 10) && (n % 625), my(k=1); while (#select(x->!isprime(x), digits(k*n)), k++); k, 0); \\ Michel Marcus, Apr 21 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Metin Sariyar, Apr 13 2021
STATUS
approved