A125146 Primes p such that (p + nextprime + p) and also (p + previousprime + p) are primes.

5, 13, 17, 103, 197, 227, 787, 823, 911, 919, 1153, 1409, 1487, 1723, 2087, 2647, 2767, 2999, 3001, 3389, 6089, 6781, 6827, 7877, 9463, 10391, 10789, 11117, 11447, 11971, 13523, 13537, 13711, 13807, 14087, 14489, 16063, 18191, 21059, 23371, 25717

Offset

1,1

Comments

First pairs of two successive primes in the sequence are {13, 17}, {911, 919}, {2999, 3001} (twin primes!), {13523, 13537}, {52543, 52553}.

First case of three successive primes is {78059, 78079, 78101}.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

13 is a term because 13 + 17 + 13 = 43 and 13 + 11 + 13 = 37 are primes.

Maple

Primes:= select(isprime, [2, seq(i, i=3..10^5, 2)]):
Primes[select(t -> isprime(2*Primes[t]+Primes[t-1]) and isprime(2*Primes[t]+Primes[t+1]), [$2..nops(Primes)-1])]; # Robert Israel, Mar 15 2018

Mathematica

pQ[n_]:=PrimeQ[2n+NextPrime[n]]&&PrimeQ[2n+NextPrime[n, -1]]; Select[ Prime[Range[2, 3000]], pQ]  (* Harvey P. Dale, Apr 25 2011 *)

Crossrefs

Sequence in context: A361563 A195549 A294132 * A051900 A275800 A347475

Adjacent sequences: A125143 A125144 A125145 * A125147 A125148 A125149

Keyword

nonn

Author

Zak Seidov, Jan 11 2007

Status

approved