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A125146 Primes p such that (p + nextprime + p) and also (p + previousprime + p) are primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A145040 A195549 A294132 * A051900 A275800 A347475

Adjacent sequences:  A125143 A125144 A125145 * A125147 A125148 A125149

KEYWORD

nonn

AUTHOR

Zak Seidov, Jan 11 2007

STATUS

approved

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)