A338570 Primes p such that q*r mod p is prime, where q is the prime preceding p and r is the prime following p.

11, 13, 19, 29, 31, 37, 47, 53, 59, 67, 73, 83, 89, 109, 127, 131, 151, 163, 173, 179, 211, 239, 251, 263, 269, 283, 307, 337, 359, 373, 383, 421, 433, 443, 449, 467, 479, 499, 503, 523, 541, 547, 569, 593, 599, 607, 653, 659, 677, 757, 787, 797, 829, 853, 877, 907, 919, 947, 967, 971, 977, 1033

Offset

1,1

Comments

Primes p such that -A049711(p)*A013632(p) mod p is prime.

Includes primes p such that p-8, p-2 and p+4 are also prime. Dickson's conjecture implies that there are infinitely many of these.

Links

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

Example

a(3) = 19 is a member because 19 is prime, the previous and following primes are 17 and 23, and (17*23) mod 19 = 11 is prime.

Maple

R:= NULL: p:= 0: q:= 2: r:= 3:
count:= 0:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  if isprime(p*r mod q) then count:= count+1; R:= R, q;  fi;
od:
R;

Crossrefs

Cf. A013632, A049711, A338566, A338567.

Sequence in context: A342406 A109650 A284037 * A321891 A153421 A050265

Adjacent sequences: A338567 A338568 A338569 * A338571 A338572 A338573

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 02 2020

Status

approved