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

0,3

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

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 *)

Prog

(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

Crossrefs

Cf. A073658, A080478, A100208.

Sequence in context: A352844 A095168 A130479 * A094181 A004730 A332460

Adjacent sequences: A272875 A272876 A272877 * A272879 A272880 A272881

Keyword

nonn,look

Author

Thomas Ordowski, May 08 2016

Extensions

More terms from Michel Marcus, May 08 2016

Status

approved