A367318 Lesser of twin primes p such that p and p+2 are both in A115591.

191, 311, 1487, 1871, 2711, 2999, 3167, 3767, 4967, 5519, 7559, 8087, 10271, 11351, 11831, 13679, 15647, 18311, 18911, 21647, 22271, 22367, 23687, 25799, 26711, 27239, 27527, 27791, 29399, 29879, 31727, 31847, 33287, 34367, 35591, 38447, 38567, 40127, 40847, 42071

Offset: 1

Author

Amiram Eldar, Nov 14 2023

Keywords

• nonn

Comments

Primes p such that p+2 is also a prime and (p-1)/ord(2, p) = (p+1)/ord(2, p+2) = 2, where ord(2,k) is the multiplicative order of 2 modulo k.

Equivalently, lesser of twin primes p such that ord(2, p+2) = ord(2, p) + 1,

Equal consecutive values in A001917 that correspond to twin primes (p, p+2) are either 1 if p is in A319248, or 2 if p is in this sequence.

Terms are congruent to 23 modulo 24. - Jianing Song, Nov 01 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A001359 and A115591.

Cf. A001122, A001917, A002326, A014664, A319248, A333743.

Programs

Mathematica

Select[Prime[Range[2, 4400]], PrimeQ[# + 2] && MultiplicativeOrder[2, # + 2] == MultiplicativeOrder[2, #] + 1 &]

PARI

is(n) = isprime(n) && isprime(n+2) && znorder(Mod(2, n + 2)) == znorder(Mod(2, n)) + 1;