A126334 -id:A126334 - cp's OEIS frontend

A168536 The lesser of twin primes p such that p*q+a+b+c are also the lesser of twin primes, (p and q are twin primes, p+2=q, a=p-1,b=(p+q)/2,c=q+1).

11, 101, 179, 347, 569, 1049, 1229, 1301, 1487, 1667, 3557, 4127, 6089, 6761, 8627, 9041, 10067, 11939, 12251, 14321, 19421, 25847, 28571, 29207, 30011, 30869, 31541, 33329, 33587, 36791, 38459, 39509, 39839, 40427, 43049, 49529, 50591, 50969

Offset: 1

Vladimir Joseph Stephan Orlovsky, Nov 28 2009

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001359, A126334, A128550, A128551

lst={};Do[p=Prime[n];q=p+2;If[PrimeQ[q],a=p-1;b=p+1;c=q+1;If[PrimeQ[p*q+a+b+c]&&PrimeQ[p*q+a+b+c+2],AppendTo[lst,p]]],{n,8!}];lst
Select[Partition[Prime[Range[5300]],2,1],#[[2]]-#[[1]]==2&&AllTrue[#[[1]]^2+5#[[1]]+{3,5},PrimeQ]&][[;;,1]] (* Harvey P. Dale, Sep 23 2023 *)

A126108 Numbers n such that n^2-2 and (n+2)^2-2 are primes.

Original entry on oeis.org

3, 5, 7, 13, 19, 27, 33, 35, 47, 61, 69, 75, 117, 119, 231, 237, 257, 265, 299, 301, 313, 335, 355, 357, 441, 447, 467, 489, 495, 523, 573, 607, 713, 761, 943, 993, 1021, 1069, 1071, 1141, 1147, 1175, 1231, 1239, 1251, 1265, 1287, 1357, 1363, 1365, 1391, 1461

Offset: 1

Zak Seidov, Mar 11 2007

nonn

The number of such n's <= 10^n: 3, 12, 36, 216, 1279,... Cf A126334 for prime n's.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A126334.

Select[Range[10^5], PrimeQ[#^2-2] && PrimeQ[(#+2)^2-2]&]

cp's OEIS Frontend

A168536 The lesser of twin primes p such that p*q+a+b+c are also the lesser of twin primes, (p and q are twin primes, p+2=q, a=p-1,b=(p+q)/2,c=q+1).

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