A343973 Primes p such that both p-1 and p+1 are in A093641.

2, 3, 5, 7, 11, 13, 23, 47, 193, 383

Offset: 1

Author

J. M. Bergot and Robert Israel, May 05 2021

Keywords

• nonn
• more

Comments

Primes p such that p-1 and p+1 each have at most one odd prime factor (counted with multiplicity).

Terms > 3 must be either of the form 3*2^k+1 with 3*2^(k-1)+1 prime, or of the form 3*2^k-1 with 3*2^(k-1)-1 prime.

There are no more terms up to 3*2^5000+1.

Conjecture: these are all the terms.

Examples

			a(5) = 11 is a term because 11-1=5*2^1 and 11+1=3*2^2 with 11, 5 and 3 prime.
		

Crossrefs

Cf. A093641.

Programs

Maple

{3,7} union select(t -> isprime(t) and isprime((t+1)/2), {seq(3*2^k+1,k=1..3000)})
union select(t -> isprime(t) and isprime((t-1)/2), {seq(3*2^k-1,k=1..3000)});