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%I #18 Feb 27 2021 11:38:40
%S 7,13,37,61,113,181,281,359,557,593,787,863,1069,1163,1213,1439,1511,
%T 1733,1831,2069,2347,2903,3011,3271,3739,4139,4409,4561,4783,4937,
%U 6221,6317,6359,6659,6857,8111,8231,8387,8521,8753,9311,10007,10453
%N Numbers of the form prime(prime(n)+1), with n satisfying prime(n)+2 = prime(n+1).
%C Also, prime numbers p such that there exists a positive integer n with the property that p is the only prime satisfying prime(prime(n)) < p < prime(prime(n+1)).
%H Harvey P. Dale, <a href="/A088985/b088985.txt">Table of n, a(n) for n = 1..1000</a>
%e prime(3) + 2 = prime(4), hence prime(prime(3)+1) = 13 is in the sequence.
%t a={};For[n=1,n<210,n++,If[Prime[n+1]==Prime[n]+2, AppendTo[a, Prime[Prime[n]+1]]]]; a
%t Prime[#+1]&/@Select[Partition[Prime[Range[300]],2,1],#[[2]]-#[[1]] == 2&][[All,1]] (* _Harvey P. Dale_, Feb 27 2021 *)
%o (PARI) pipprimes(n) = { for(x=1,n, c=0; p1 = prime(prime(x)); p2 = prime(prime(x+1)); forprime(y=p1+2,p2-2,c++); if(c==1, forprime(y=p1+2,p2-2, print1(y","); ); ) ) }
%K nonn
%O 1,1
%A _Cino Hilliard_, Oct 31 2003
%E Edited by _Stefan Steinerberger_, Jul 27 2007
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