A080174 Primes prime(k) such that prime(k)*k falls between twin primes.

3, 113, 359, 827, 2069, 2267, 3643, 5179, 7829, 9029, 10223, 10369, 11777, 18169, 21143, 22409, 23173, 23957, 25411, 28051, 28447, 29251, 31991, 32717, 34487, 38561, 43133, 54323, 57097, 61363, 73043, 82493, 86269, 94099

Offset

1,1

Comments

Also primes p such that pi(p)*p falls between twin primes (see Crossrefs).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

113 is in the list because 113 is the 30th prime and 113*30=3390 falls between the twin primes 3389 and 3391.

Mathematica

Prime[Select[Range[10000], PrimeQ[Prime[#]# - 1] && PrimeQ[Prime[#]# + 1] &]] (* Alonso del Arte, Jul 05 2011 *)

Prog

(PARI) v=List(); k=0; forprime(p=2, 1e5, if(isprime(k++*p+1)&&isprime(k*p-1), listput(v, p))); Vec(v)
(Magma) [NthPrime(n): n in [1..10^4] | IsPrime(NthPrime(n)*n-1) and IsPrime(NthPrime(n)*n+1)];  // Bruno Berselli, Jul 06 2011

Crossrefs

The sequence is the intersection of A062291 and A192611.

Cf. A000720 pi(n), the number of primes <= n.

Cf. A001359 Lesser of twin primes; A006512 Greater of twin primes.

Cf. A014574 Average of twin prime pairs.

Sequence in context: A350053 A249164 A341047 * A065117 A227794 A225334

Adjacent sequences: A080171 A080172 A080173 * A080175 A080176 A080177

Keyword

nonn

Author

Andrea Raffetti, Jul 05 2011

Extensions

Additional terms from Bruno Berselli, Jul 05 2011

Status

approved