A065117 Primes such that prime(p) +- pi(p) are simultaneously prime.

3, 113, 463, 593, 743, 1109, 2473, 4139, 4657, 4937, 5531, 5879, 6473, 6581, 6659, 6701, 7297, 7529, 8387, 8521, 8929, 9349, 10369, 10499, 12289, 12829, 13411, 13697, 14033, 14323, 15907, 18637, 19391, 19841, 21143, 21647, 23021, 27077

Offset

1,1

Comments

Intersection of A065059 and A065060.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

113 is in the sequence because PrimePi(113) is 30, Prime(113) is 617, and both 587 and 647 are primes.

Mathematica

Do[p0 = Prime[ Prime[n]]; p1 = PrimePi[ Prime[n]]; If[ PrimeQ[p0 + p1] && PrimeQ[p0 - p1], Print[ Prime[n]]], {n, 1, 5000} ]
spQ[n_]:=Module[{p=PrimePi[n]}, AllTrue[Prime[n]+{p, -p}, PrimeQ]]; Select[ Prime[ Range[10000]], spQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 03 2018 *)

Prog

(PARI) { n=0; default(primelimit, 4294965247); for (m=1, 10^9, p=prime(m); p0 = prime(p); p1 = primepi(p); if (isprime(p0 + p1) && isprime(p0 - p1), write("b065117.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 10 2009

Crossrefs

Cf. A065059, A065060.

Sequence in context: A249164 A341047 A080174 * A227794 A225334 A240441

Adjacent sequences: A065114 A065115 A065116 * A065118 A065119 A065120

Keyword

nonn

Author

Robert G. Wilson v, Nov 12 2001

Extensions

Example corrected by Harvey P. Dale, Sep 03 2018

Status

approved