A255581 Numbers prime(n) such that prime(n)^2 + prime(n+1)^2 - prime(n+2)^2 is prime.
13, 23, 29, 37, 41, 43, 59, 61, 67, 71, 79, 89, 97, 103, 109, 137, 149, 173, 193, 197, 223, 227, 239, 269, 271, 307, 311, 313, 349, 353, 383, 409, 463, 467, 479, 487, 491, 521, 541, 547, 571, 577, 607, 613, 617, 619, 653, 659, 661, 691, 809, 821, 823, 857
Offset: 1
Keywords
Examples
13 belongs to the sequence as 13 is prime, 13 is the 6th prime number, the 7th prime is 17, the 8th prime is 19, and 13^2 + 17^2 - 19^2 = 97, which is prime. 31 does not belong to the sequence as 31^2 + 37^2 - 41^2 = 649 and 649 is not prime.
Programs
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Maple
A255581:=n->`if`(isprime(ithprime(n)^2+ithprime(n+1)^2-ithprime(n+2)^2), ithprime(n), NULL): seq(A255581(n), n=1..200); # Wesley Ivan Hurt, Feb 28 2015
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Octave
p=primes(500); for i=1:100 ris=(p(i))^2+(p(i+1))^2-(p(i+2))^2; if ris>0 if isprime(ris) disp(p(i)); end end end
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PARI
lista(nn) = {forprime(p=2, nn, q = nextprime(p+1); r = nextprime(q+1); if (isprime(p^2+q^2-r^2), print1(p, ", ")););} \\ Michel Marcus, Mar 01 2015