A069227 a(1)=1, a(2)=2; a(n+2) = (a(n+1) + a(n))/b(n) where b(n) = gcd(a(n+1) + a(n), 4).

1, 2, 3, 5, 2, 7, 9, 4, 13, 17, 15, 8, 23, 31, 27, 29, 14, 43, 57, 25, 41, 33, 37, 35, 18, 53, 71, 31, 51, 41, 23, 16, 39, 55, 47, 51, 49, 25, 37, 31, 17, 12, 29, 41, 35, 19, 27, 23, 25, 12, 37, 49, 43, 23, 33, 14, 47, 61, 27, 22, 49, 71, 30, 101, 131, 58, 189, 247, 109, 89

Offset

1,2

Comments

A Collatz-Fibonacci mixture.

Conjecture: sequence diverges to infinity (a(500)=151767071).

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

a(18)=43, a(19)=57, so gcd(a(18) + a(19), 4) = 4 and hence a(20) = 100/4 = 25.

Mathematica

Nest[Append[#, #/GCD[#, 4] &[#[[-1]] + #[[-2]]]] &, {1, 2}, 68] (* Ivan Neretin, Jun 28 2017 *)
nxt[{a_, b_}]:={b, (a+b)/GCD[a+b, 4]}; NestList[nxt, {1, 2}, 70][[All, 1]] (* Harvey P. Dale, Jan 16 2020 *)

Crossrefs

Sequence in context: A231233 A174562 A224382 * A117368 A355091 A137826

Adjacent sequences: A069224 A069225 A069226 * A069228 A069229 A069230

Keyword

nonn

Author

Benoit Cloitre, Apr 12 2002

Status

approved