A165262 Sorted hypotenuses with no repeats of Primitive Pythagorean Triples (PPT) if sum of all 3 sides are averages of twin prime pairs.

5, 13, 85, 113, 145, 197, 221, 241, 349, 457, 541, 569, 625, 821, 829, 841, 1025, 1037, 1093, 1157, 1241, 1433, 1465, 1621, 1741, 1769, 2029, 2069, 2249, 2353, 2441, 2465, 2501, 2669, 2725, 2801, 2809, 2825, 2873, 3029, 3077, 3221, 3293, 3305, 3389, 3889

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

Triples begin 3,4,5; 5,12,13; 15,112,113; 21,220,221; 24,143,145; 28,195,197; 36,77,85; 41,840,841; 59,1740,1741; 64,1023,1025; 89,3960,3961; 100,2499,2501; ...
So with sorted hypotenuses:
  3 +  4 +  5 = 12, and 11 and 13 are twin primes;
  5 + 12 + 13 = 30, and 29 and 31 are twin primes; ...

Mathematica

amax=10^5; 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; b=2*m*n; If[GCD[a, b]==1, If[a>b, {a, b}={b, a}]; If[a>amax, Break[]]; c=m^2+n^2; x=a+b+c; If[PrimeQ[x-1]&&PrimeQ[x+1], k++; AppendTo[lst, c]]]], {m, n+1, 12!, 2}], {n, 1, q, 1}]; Union@lst

Crossrefs

Cf. A009004, A020882, A020883, A165158, A165159, A165160, A165236, A165237, A165238, A165260, A165261.

Sequence in context: A363015 A324418 A359316 * A092955 A190949 A263468

Adjacent sequences: A165259 A165260 A165261 * A165263 A165264 A165265

Keyword

nonn,uned

Author

Vladimir Joseph Stephan Orlovsky, Sep 11 2009

Status

approved