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

1,1

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.

Links

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A001359 and A115591.

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

Sequence in context: A046010 A146361 A229075 * A142806 A142086 A070831

Adjacent sequences: A367315 A367316 A367317 * A367319 A367320 A367321

Keyword

nonn

Author

Amiram Eldar, Nov 14 2023

Status

approved