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

%I A342992 #60 Apr 22 2021 22:16:40
%S A342992 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,
%T A342992 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,
%U A342992 4,43,5,42,5,4,8,0,5,1,1,3,1,7,1,74,3,0,93
%N A342992 Smallest k such that k*n contains only prime digits, or 0 if no such k exists.
%C A342992 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.
%C A342992 Conjecture: a(n) > 0 for all n that are not divisible by 5.
%C A342992 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
%H A342992 David A. Corneth, <a href="/A342992/b342992.txt">Table of n, a(n) for n = 1..10000</a>
%H A342992 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?curio_id=41432">Prime Curios! 56479</a>
%e A342992 a(4) = 8 because 8 is the smallest number k such that 8*4 = 32 contains only prime digits.
%o A342992 (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
%Y A342992 Cf. A046034, A227922, A276729, A300289.
%K A342992 nonn,base
%O A342992 1,1
%A A342992 _Metin Sariyar_, Apr 13 2021