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

1,1

Comments

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

Links

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

Example

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.

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)]);

Prog

(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

Crossrefs

Cf. A007605, A053666, A136251.

Sequence in context: A232726 A029541 A068714 * A036267 A107934 A356087

Adjacent sequences: A344124 A344125 A344126 * A344128 A344129 A344130

Keyword

nonn,base

Author

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

Status

approved