A334026 Primes p such that 2*p and 4*p are 1 away from a prime.

2, 3, 5, 7, 11, 37, 41, 53, 79, 83, 97, 131, 139, 173, 199, 281, 293, 307, 431, 499, 577, 593, 619, 683, 727, 743, 911, 997, 1013, 1297, 1429, 1481, 1511, 1811, 1901, 1931, 2003, 2029, 2141, 2273, 2351, 2693, 3037, 3067, 3109, 3491, 3499, 3739, 3769, 3863, 3911, 4211, 4373, 4447, 4481, 4567, 4871

Offset: 1

Author

Robert Israel, Apr 12 2020

Keywords

• nonn

Comments

Primes p such that at least one of 2*p-1 and 2*p+1 is prime, and at least one of 4*p-1 and 4*p+1 is prime.

Primes p such that either 2*p-1 and 4*p+1 are prime, or 2*p+1 and 4*p-1 are prime.

Primes p such that 4*p is in A333197.

Examples

			a(3) = 5 is a member because 5, 2*5+1=11 and 4*5-1=19 are primes.
		

Links

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

Crossrefs

Cf. A120628, A333197.

Programs

Maple

filter:= proc(t) isprime(t) and (isprime(2*t+1) or isprime(2*t-1)) and (isprime(4*t+1) or isprime(4*t-1)) end proc:
select(filter, [2,seq(i,i=3..10000,2)]);

Mathematica

Select[Prime[Range[700]],AnyTrue[2#+{1,-1},PrimeQ]&&AnyTrue[4#+{1,-1},PrimeQ] &] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 17 2021 *)