A342992 Smallest k such that k*n contains only prime digits, or 0 if no such k exists.

2, 1, 1, 8, 1, 12, 1, 4, 3, 0, 2, 6, 4, 18, 5, 2, 15, 4, 3, 0, 12, 1, 1, 3, 1, 2, 1, 9, 8, 0, 12, 1, 1, 8, 1, 2, 1, 14, 7, 0, 13, 6, 54, 8, 5, 7, 5, 49, 15, 0, 5, 1, 1, 43, 1, 42, 1, 4, 43, 0, 12, 6, 4, 43, 5, 42, 5, 4, 8, 0, 5, 1, 1, 3, 1, 7, 1, 74, 3, 0, 93

Offset: 1

Author

Metin Sariyar, Apr 13 2021

Keywords

• nonn
• base

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

Examples

			a(4) = 8 because 8 is the smallest number k such that 8*4 = 32 contains only prime digits.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 56479

Crossrefs

Cf. A046034, A227922, A276729, A300289.

Programs

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