A340564 Primes p such that the sum of (p mod q) for primes q < p is prime.

5, 13, 23, 113, 137, 151, 163, 251, 317, 461, 479, 487, 521, 661, 691, 719, 887, 907, 991, 1129, 1213, 1453, 1901, 1949, 1987, 2053, 2141, 2243, 2333, 2399, 2549, 2797, 3041, 3049, 3119, 3221, 3433, 3457, 3527, 3529, 3691, 3697, 3911, 4013, 4241, 4649, 4817, 5099, 5407, 5413, 5689, 5693, 6217

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 11 2021

Keywords

• nonn

Comments

a(n) = prime(m) if A033955(m) is prime.

Examples

			a(3) = 23 is a term because (23 mod 2) + ... + (23 mod 19) = 1+2+3+2+1+10+6+4 = 29 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A033955.

Programs

Maple

f:= proc(n) local i,p;
  p:= ithprime(n);
  add(p mod ithprime(i),i=1..n-1)
end proc:
map(ithprime, select(t -> isprime(f(t)), [$1..2000]));

PARI

isok(p) = if (isprime(p), my(s=0); forprime(q=2, precprime(p-1), s += p % q); isprime(s);); \\ Michel Marcus, Jan 11 2021