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%I #43 Mar 19 2023 05:01:28
%S 3,113,359,827,2069,2267,3643,5179,7829,9029,10223,10369,11777,18169,
%T 21143,22409,23173,23957,25411,28051,28447,29251,31991,32717,34487,
%U 38561,43133,54323,57097,61363,73043,82493,86269,94099
%N Primes prime(k) such that prime(k)*k falls between twin primes.
%C Also primes p such that pi(p)*p falls between twin primes (see Crossrefs).
%H Charles R Greathouse IV, <a href="/A080174/b080174.txt">Table of n, a(n) for n = 1..10000</a>
%e 113 is in the list because 113 is the 30th prime and 113*30=3390 falls between the twin primes 3389 and 3391.
%t Prime[Select[Range[10000], PrimeQ[Prime[#]# - 1] && PrimeQ[Prime[#]# + 1] &]] (* _Alonso del Arte_, Jul 05 2011 *)
%o (PARI) v=List();k=0; forprime(p=2, 1e5, if(isprime(k++*p+1)&&isprime(k*p-1),listput(v,p))); Vec(v)
%o (Magma) [NthPrime(n): n in [1..10^4] | IsPrime(NthPrime(n)*n-1) and IsPrime(NthPrime(n)*n+1)]; // _Bruno Berselli_, Jul 06 2011
%Y The sequence is the intersection of A062291 and A192611.
%Y Cf. A000720 pi(n), the number of primes <= n.
%Y Cf. A001359 Lesser of twin primes; A006512 Greater of twin primes.
%Y Cf. A014574 Average of twin prime pairs.
%K nonn
%O 1,1
%A _Andrea Raffetti_, Jul 05 2011
%E Additional terms from _Bruno Berselli_, Jul 05 2011
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