A088483 -id:A088483 - cp's OEIS frontend

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

2, 3, 11, 71, 227, 491, 683, 1103, 1187, 2591, 3923, 4271, 4931, 6737, 7193, 7703, 8093, 8753, 8963, 9173, 9377, 10271, 13043, 13451, 13997, 15233, 15443, 15803, 15887, 17957, 18701, 19961, 20681, 21701, 22031, 22073, 24371, 24473, 24683

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

nonn

p=1, q=2(prime), a=3, b=4, c=5, s=12-+1 primes, ...

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150, A155186, A068231, A129517, A054574, A132281.

lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;ar=a*b/2;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[q],AppendTo[lst,q]]],{n,8!}];lst

A228978 Primes p such that p and p+2, p^2+p-1 and p^2+p+1, and (p^2+p-1)^2+p^2+p-2 and (p^2+p-1)^2+p^2+p are three pairs of twin primes.

Original entry on oeis.org

11767181, 35057849, 84428051, 91460249, 105929711, 115401719, 162790781, 197352401, 217761851, 235863209, 266250839, 284597741, 370000511, 386278019, 554761451, 576412271, 581549669, 592975109, 611599661, 625806761, 626450411, 655727771, 670280591, 680468669, 744737111, 883687349, 1085880641, 1119813311, 1139369111

Offset: 1

Pierre CAMI, Sep 10 2013

nonn

Subsequence of A228968.

Cf. A088483, A228968.

tptpQ[n_]:=Module[{p2=n^2+n},AllTrue[{p2-1,p2+1,(p2-1)^2+p2-2,(p2-1)^2+ p2},PrimeQ]]; Select[Transpose[Select[Partition[ Prime[ Range[ 58*10^6]],2,1], #[[2]]-#[[1]]==2&]][[1]],tptpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 10 2014 *)

Corrected by Harvey P. Dale, Nov 10 2014

cp's OEIS Frontend

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

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A228978 Primes p such that p and p+2, p^2+p-1 and p^2+p+1, and (p^2+p-1)^2+p^2+p-2 and (p^2+p-1)^2+p^2+p are three pairs of twin primes.

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cp's OEIS Frontend

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes.

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A228978 Primes p such that p and p+2, p^2+p-1 and p^2+p+1, and (p^2+p-1)^2+p^2+p-2 and (p^2+p-1)^2+p^2+p are three pairs of twin primes.

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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.