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A281022 Single (or isolated or non-twin) primes that are also safe primes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..50.

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.

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 A039374

Adjacent sequences:  A281019 A281020 A281021 * A281023 A281024 A281025

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Jan 13 2017

STATUS

approved

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Last modified October 21 02:29 EDT 2021. Contains 348141 sequences. (Running on oeis4.)