A284035 Upper twin primes which correspond to the hypotenuse in a Pythagorean triple whose short leg is also a prime.

5, 13, 61, 181, 421, 3121, 5101, 60901, 83641, 100801, 135721, 161881, 163021, 218461, 273061, 491041, 595141, 637321, 697381, 1064341, 1108561, 1171981, 1806901, 2574181, 2601481, 2740141, 2763601, 2853661, 3248701, 3535141, 3567121, 3696481, 3723721, 3729181, 4832941

Offset: 1

Author

Giuseppe Coppoletta, Mar 19 2017

Keywords

• nonn

Comments

A284034 gives the corresponding short leg primes in the definition.

Examples

			The prime q = 3121 is in the sequence because q - 2 = 3119 is prime and {79, 3120, 3121} is a Pythagorean triple with prime short leg (see example in A284034).
		

Crossrefs

Cf. A051859, A067756, A284034.

Programs

PARI

lista(nn) = forprime(p=3, nn, if (isprime(p) && isprime((p^2-3)/2) && isprime(q=(p^2+1)/2), print1(q, ", "))); \\ Michel Marcus, Apr 01 2017

Formula

A284034(n)^2 + (a(n) - 1)^2 = a(n)^2, i.e., a(n) = (A284034(n)^2 + 1)/2.

Extensions

More terms from Michel Marcus, Apr 01 2017