A350401 Primes p such that if q is the next prime, p*q mod (A004086(p)+A004086(q)) is prime.

3, 5, 7, 11, 13, 23, 29, 31, 53, 59, 71, 73, 83, 89, 101, 107, 109, 127, 137, 149, 163, 173, 181, 191, 193, 211, 223, 227, 233, 239, 257, 271, 277, 281, 283, 307, 317, 367, 373, 389, 409, 419, 431, 449, 461, 463, 467, 479, 491, 509, 521, 523, 547, 577, 587, 593, 607, 613, 631, 641, 643, 653, 659

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 28 2021

Keywords

• nonn
• base

Examples

			a(6) = 23 is a member because it is prime, the next prime is 29, and 23*29 mod (32+92) = 667 mod 124 = 47 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004086.

Programs

Maple

revdigs:= proc(n) local L,i,m;
  L:= convert(n,base,10); m:= nops(L);
  add(L[i]*10^(m-i),i=1..m)
end proc:
q:= 2: qr:= 2:
R:= NULL: count:= 0:
while count < 100 do
  p:=q; pr:= qr;
  q:= nextprime(p); qr:= revdigs(q); s:= p*q mod (pr+qr);
  if isprime(s) then
     R:= R, p; count:= count+1;
  fi
od:
R;