A000978 -id:A000978 - cp's OEIS frontend

A283191 Prime numbers p such that (2^p - 5)/3 is prime.

7, 13, 19, 31, 373, 811, 1117, 5059, 12601

Offset: 1

Dmitry Ezhov, Mar 02 2017

Let W = (2^p - 5)/3 and s = (W+1)/(2*p), then 5^s == 2 (mod W) for terms 1..9.
Subsequence of 7, 13, 19, 31, 51, 55, 85, 111, 319, 373,.. which are numbers m such that (2^m-5)/3 is prime. - R. J. Mathar, Mar 05 2017
a(10) > 3*10^5. - Michael S. Branicky, Jan 30 2025

Cf. A000978.

Select[Prime@ Range[2, 1000], PrimeQ[(2^# - 5)/3] &] (* Michael De Vlieger, Mar 03 2017 *)

forprime(p=3, 30000, W= (2^p-5)/3; if(ispseudoprime(W), print1(p, ", ")))

A290246 Prime numbers that are common indices to both prime Lucas and prime Wagstaff numbers.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 31, 61, 79, 313, 10691

Offset: 1

Amiram Eldar, Jul 24 2017

Prime numbers p such that Lucas(p) and (2^p + 1)/3 are both primes.

Intersection of A000978 and A001606.

Cf. A000978, A001606, A080327.

seq = {}; wagstaff[n_] := (2^n + 1)/3; Do[p = Prime[n]; If[PrimeQ[LucasL[p]] && PrimeQ[wagstaff[p]], AppendTo[seq, p]], {n, 1, 1304}]; seq

cp's OEIS Frontend

A283191 Prime numbers p such that (2^p - 5)/3 is prime.

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