A333327 Primes p such that, if p = Sum_{0<=i<=k} d_i*10^i is the decimal expansion, p mod (d_i*10^i) is prime for 0<=i<=k.

17, 23, 37, 47, 53, 83, 113, 317, 353, 367, 397, 443, 467, 479, 647, 653, 683, 743, 773, 953, 983, 997, 1223, 1283, 1367, 1373, 1433, 1523, 1823, 1997, 2137, 2467, 2677, 2887, 3167, 3389, 3617, 3727, 3967, 4283, 4349, 4523, 4643, 5197, 5827, 5839, 5857, 6113, 6173, 6317, 6337, 6353, 6653, 6863

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 15 2020

Keywords

• nonn
• base

Comments

No digits are 0. Last digit is not 1.

Examples

			a(7) = 113 is a term because 113, 113 mod 100 = 13, 113 mod 10 = 3, and 113 mod 3 = 2 are all prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Contained in A227916.

Programs

Maple

filter:= proc(p) local L;
  if not isprime(p) then return false fi;
  L:= convert(p,base,10);
  if has(0,L) then return false fi;
  andmap(i -> isprime(p mod (L[i]*10^(i-1))), [$1..nops(L)])
end proc:
select(filter, [seq(i,i=13..10000,2)]);