A358342 Lesser of twin primes p such that sigma((p-1)/2) + tau((p-1)/2) is a prime.

3, 5, 17, 65537, 1927561217, 6015902625062501, 12370388895062501, 835920078368222501, 6448645485213008897, 50973659693056000001, 54332889713542767617, 64304984013657011717, 112112769248058062501, 147337258721536000001

Offset: 1

Author

Jaroslav Krizek, Nov 10 2022

Keywords

• nonn
• more

Comments

Lesser of twin primes p such that A000203((p-1)/2) + A000005((p-1)/2) is a prime q.

The first 4 terms are Fermat primes from A019434.

Corresponding values of primes q: 2, 5, 19, 65551, 2248681529, ...

Subsequence of A272060 and A272061.

Lesser of twin primes of the form 2*m+1 with m a term of A064205.

There are no other terms <= 10^14.

All the terms above 3 are in A145824. - Amiram Eldar, Jan 05 2023

Examples

			17 and 19 are twin primes; sigma((17-1)/2) + tau((17-1)/2) = sigma(8) + tau(8) = 15 + 4 = 19; 19 is prime, so 17 is in the sequence.
		

Crossrefs

Intersection of A001359 and A272061.

Cf. A000005 (tau), A000203 (sigma), A019434, A064205, A145824, A272060.

Programs

Magma

[n: n in [3..10^7] | IsPrime(n) and IsPrime(n+2) and IsPrime(&+Divisors((n-1) div 2) + #Divisors((n-1) div 2))]

Mathematica

Join[{3}, Select[4*Range[25000]^2 + 1, PrimeQ[#] && PrimeQ[# + 2] && PrimeQ[DivisorSigma[1, (# - 1)/2] + DivisorSigma[0, (# - 1)/2]] &]]
(* or *)
A272061 = Cases[Import["https://oeis.org/A272061/b272061.txt", "Table"], {, }][[;; , 2]]; Select[A272061, PrimeQ[# + 2] &] (* Amiram Eldar, Jan 05 2023 *)

PARI

isok(p) = if (isprime(p) && isprime(p+2), my(f=factor((p-1)/2)); isprime(sigma(f)+numdiv(f))); \\ Michel Marcus, Nov 23 2022