A112957 a(1) = a(2) = a(3) = 1; for n > 1, a(n+3) = a(n)^2 + a(n+1)^2 + a(n+2)^2.

1, 1, 1, 3, 11, 131, 17291, 298995963, 89398586189293211, 7992107212644486930829797919966571, 63873777698404030240264509605345282496735163325301838600463378485931

Offset: 1

Author

Jonathan Vos Post, Jan 02 2006; definition corrected Jan 02 2006

Keywords

• easy
• nonn

Comments

A quadratic tribonacci sequence.

This is to A000283 as a tribonacci (A000213) is to Fibonacci. Two oddities about this sequence: (a) its first 7 terms are identical to terms numbered 2 through 8 of A072878; (b) only one of the first 9 terms are composite. Primes in the sequence begin 3, 11, 131, 17291 and 89398586189293211. What is the next prime?

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A000213, A000283, A072878, A112958, A112959, A112960.

Programs

Mathematica

Join[{a=1,b=1,c=1},Table[d=a*a+b*b+c*c;a=b;b=c;c=d,{n,10}]] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)