A155173 - OEIS

A155173

Short leg A of primitive Pythagorean triangles such that perimeter s is average of twin prime pairs, q=p+1, A=q^2-p^2, C=q^2+p^2, B=2*p*q, s=A+B+C; s -/+ 1 are primes.

3, 5, 15, 21, 41, 59, 89, 101, 131, 141, 153, 155, 203, 209, 215, 231, 309, 351, 395, 405, 453, 455, 495, 551, 743, 761, 825, 915, 981, 1001, 1149, 1193, 1295, 1343, 1365, 1421, 1529, 1659, 1853, 2105, 2171, 2205, 2255, 2373, 2409, 2411, 2451, 2513, 2561, 2649

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OFFSET

1,1

COMMENTS

Odd numbers k such that k^2+k+1 and k^2+k-1 are both prime. - Robert Israel, Feb 07 2026

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

With p=1, then q=2,a=3,b=4,c=5, and s=12-+1 (11, 13) both primes.

MAPLE

select(k -> isprime(k^2+k+1) and isprime(k^2+k-1), [seq(i, i=1..10000, 2)]); # Robert Israel, Feb 07 2026

MATHEMATICA