A165237 Long legs of primitive Pythagorean triples (a,b,c) for which 2a+1, 2b+1 and 2c+1 are primes.

21, 56, 285, 483, 783, 999, 1269, 1593, 1911, 2613, 3003, 3596, 3621, 3740, 4136, 4233, 4928, 5096, 5451, 5828, 5840, 6320, 7040, 7280, 8036, 8468, 9021, 9296, 9591, 11660, 12075, 12573, 12705, 12920, 12956, 13563, 14396, 14595, 15429, 15561

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Example

See A165236.

Mathematica

amax=6*10^4; lst={}; k=0; q=12!; Do[If[(e=((n+1)^2-n^2))>amax, Break[]]; Do[If[GCD[m, n]==1, a=m^2-n^2; If[PrimeQ[2*a+1], b=2*m*n; If[PrimeQ[2*b+1], If[GCD[a, b]==1, If[a>b, {a, b}={b, a}]; If[a>amax, Break[]]; c=m^2+n^2; If[PrimeQ[2*c+1], k++; AppendTo[lst, b]]]]]]; If[a>amax, Break[]], {m, n+1, 12!, 2}], {n, 1, q, 1}]; Union@lst

Crossrefs

Cf. A020883, A165236, A156238.

Sequence in context: A031963 A067727 A254144 * A271734 A189004 A183310

Adjacent sequences: A165234 A165235 A165236 * A165238 A165239 A165240

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Sep 09 2009

Status

approved