A344127 Primes p such that (p mod s) and (p mod t) are consecutive primes, where s is the sum of the digits of p and t is the product of the digits of p.

23, 29, 313, 397, 431, 661, 941, 1129, 1193, 1223, 1277, 1613, 2621, 2791, 3461, 4111, 4159, 12641, 12911, 14419, 15271, 19211, 21611, 21773, 22613, 26731, 29819, 31181, 31511, 41381, 61211, 74611, 111191, 115811, 121181, 121727, 141161, 141221, 141269, 145513, 157523, 171713, 173141, 173891

Offset: 1

Author

J. M. Bergot and Robert Israel, May 09 2021

Keywords

• nonn
• base

Comments

Since p mod 0 is not defined, the digit 0 is not allowed.

Examples

			a(3) = 313 is a term because with s = 3+1+3 = 7 and t = 3*1*3 = 9, 313 mod 7 = 5 and 313 mod 9 = 7 are consecutive primes.
		

Links

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

Crossrefs

Cf. A007605, A053666, A136251.

Programs

Maple

filter:= proc(p) local L,s,t,q;
  L:= convert(p,base,10);
  s:= convert(L,`+`);
  t:= convert(L,`*`);
  if t = 0 then return false fi;
  q:= p mod s;
  isprime(q) and (p mod t) = nextprime(q)
end proc:
select(filter, [seq(ithprime(i),i=1..20000)]);

PARI

isok(p) = if (isprime(p), my(d=digits(p)); vecmin(d) && isprime(q=(p%vecsum(d))) && isprime(r=(p%vecprod(d))) && (nextprime(q+1)==r)); \\ Michel Marcus, May 10 2021