A272878 a(0) = a(1) = 1, smallest a(n+1) > a(n-1) such that a(n)^2 + a(n+1)^2 is prime.

1, 1, 2, 3, 8, 5, 16, 9, 26, 11, 30, 13, 32, 15, 34, 21, 44, 29, 46, 39, 50, 43, 60, 61, 64, 71, 66, 79, 74, 81, 100, 83, 102, 95, 104, 101, 114, 109, 134, 115, 136, 135, 146, 139, 154, 141, 160, 143, 168, 155, 172, 165, 178, 173, 190, 177, 200, 189, 206, 199

Offset: 0

Author

Thomas Ordowski, May 08 2016

Keywords

• nonn
• look

Comments

The associated primes 2, 5, 13, 73, 89, 281, 337, 757, 797, ... create a strictly increasing sequence. What is the rate of its growth?

Positive integers that are not in this sequence are 4, 6, 7, 10, 12, 14, 17, 18, 19, 20, 22, 23, 24, 25, 27, ... - Altug Alkan, May 14 2016

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A073658, A080478, A100208.

Programs

Mathematica

a[0]=1; a[1]=1; a[n_]:=a[n]= Block[{t = a[n-2] + 1}, While[! PrimeQ[t^2 + a[n-1]^2], t++]; t]; Array[a, 80, 0] (* Giovanni Resta, May 08 2016 *)

PARI

lista(nn) = {print1(x = 1, ", "); print1(y = 1, ", "); for (n=2, nn, z = x+1; while (! isprime(y^2+z^2), z++); print1(z, ", "); x = y; y = z;);} \\ Michel Marcus, May 08 2016

Extensions

More terms from Michel Marcus, May 08 2016