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%I #5 Sep 08 2022 08:45:30
%S 53,79,109,131,197,199,269,293,313,353,359,373,383,433,443,463,503,
%T 521,571,577,593,613,617,643,659,673,701,709,719,733,751,773,787,797,
%U 811,827,839,863,877,883,919,937,953,967,977,991,997,1013,1031,1033,1039
%N Primes p such that k-1, k+1 are composite, where k = absolute value of q^2 - p*r and p, q, r are consecutive primes.
%C Primes that are not in A127566.
%H Harvey P. Dale, <a href="/A129257/b129257.txt">Table of n, a(n) for n = 1..3000</a>
%e 79, 83, 89 are consecutive primes, 83^2 - 79*89 = -142. Both 141 = 3*47 and 143 = 11*13 are composite, hence 79 is a term.
%t Transpose[Select[Partition[Prime[Range[200]],3,1],AllTrue[Abs[ #[[2]]^2- #[[1]]*#[[3]]]+{1,-1},CompositeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 04 2015 *)
%o (Magma) [ p: p in PrimesInInterval(2, 1060) | not IsPrime(k-1) and not IsPrime(k+1) where k is Abs(q^2 - p*r) where r is NextPrime(q) where q is NextPrime(p) ];
%Y Cf. A127566.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Apr 08 2007
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