A281022 Single (or isolated or non-twin) primes that are also safe primes.

23, 47, 83, 167, 263, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1187, 1283, 1307, 1367, 1439, 1523, 1823, 1907, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903, 2963, 3023, 3203, 3623, 3779, 3803, 3863, 3947, 4007, 4079, 4139, 4283, 4679, 4703, 4919

Offset

1,1

Comments

Primes p such that neither p - 2 nor p + 2 is prime while (p - 1) / 2 is prime.

It is conjectured that there are infinitely many safe primes, but this is still unproved, so it is not known whether this sequence is infinite.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = 2 * A230117(n+1) + 1, for n > 0.

Example

23 is a term because 23 - 2 = 21 and 23 + 2 = 25 are composite and (23 - 1) / 2 = 11 is prime.

Mathematica

Select[Prime[Range[700]], Boole[PrimeQ[{#+2, #-2, (#-1)/2}]]=={0, 0, 1}&] (* Harvey P. Dale, Aug 14 2023 *)

Prog

(PARI) lista(nn) = { forprime(p=11, nn, if(!isprime(p+2) && isprime((p-1)/2), print1(p, ", "))); }

Crossrefs

Cf. A005385, A007510, A230117.

Sequence in context: A117876 A338386 A090191 * A054821 A195058 A352291

Adjacent sequences: A281019 A281020 A281021 * A281023 A281024 A281025

Keyword

nonn,easy

Author

Altug Alkan, Jan 13 2017

Status

approved