This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080174 #43 Mar 19 2023 05:01:28 %S A080174 3,113,359,827,2069,2267,3643,5179,7829,9029,10223,10369,11777,18169, %T A080174 21143,22409,23173,23957,25411,28051,28447,29251,31991,32717,34487, %U A080174 38561,43133,54323,57097,61363,73043,82493,86269,94099 %N A080174 Primes prime(k) such that prime(k)*k falls between twin primes. %C A080174 Also primes p such that pi(p)*p falls between twin primes (see Crossrefs). %H A080174 Charles R Greathouse IV, <a href="/A080174/b080174.txt">Table of n, a(n) for n = 1..10000</a> %e A080174 113 is in the list because 113 is the 30th prime and 113*30=3390 falls between the twin primes 3389 and 3391. %t A080174 Prime[Select[Range[10000], PrimeQ[Prime[#]# - 1] && PrimeQ[Prime[#]# + 1] &]] (* _Alonso del Arte_, Jul 05 2011 *) %o A080174 (PARI) v=List();k=0; forprime(p=2, 1e5, if(isprime(k++*p+1)&&isprime(k*p-1),listput(v,p))); Vec(v) %o A080174 (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 A080174 The sequence is the intersection of A062291 and A192611. %Y A080174 Cf. A000720 pi(n), the number of primes <= n. %Y A080174 Cf. A001359 Lesser of twin primes; A006512 Greater of twin primes. %Y A080174 Cf. A014574 Average of twin prime pairs. %K A080174 nonn %O A080174 1,1 %A A080174 _Andrea Raffetti_, Jul 05 2011 %E A080174 Additional terms from _Bruno Berselli_, Jul 05 2011