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A080174 Primes p(k) such that p(k)*k falls between twin primes. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A139929 A142603 A249164 * 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

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Last modified September 17 04:03 EDT 2019. Contains 327119 sequences. (Running on oeis4.)