A069228 a(1)=1, a(2)=4, a(n+2)=(a(n+1)+a(n))/b(n), where b(n)=gcd(a(n+1)+a(n),4).

1, 4, 5, 9, 7, 4, 11, 15, 13, 7, 5, 3, 2, 5, 7, 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

Offset

1,2

Comments

A Collatz-Fibonacci mixture. Conjecture : sequence diverges to infinity.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4)=9 a(5)=7 so gcd(a(4)+a(5),4)=4 and hence a(6)=16/4=4.

Maple

f:= proc(n) option remember;
  (procname(n-1)+procname(n-2))/igcd(procname(n-1)+procname(n-2), 4)
end proc:
f(1):= 1: f(2):= 4:
map(f, [$1..100]); # Robert Israel, Jan 05 2018

Mathematica

a[n_] := a[n] = Switch[n, 1, 1, 2, 4, _, (a[n-1] + a[n-2])/GCD[a[n-1] + a[n-2], 4]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, May 17 2023 *)

Crossrefs

Sequence in context: A030139 A356509 A371936 * A200354 A328485 A021689

Adjacent sequences: A069225 A069226 A069227 * A069229 A069230 A069231

Keyword

nonn

Author

Benoit Cloitre, Apr 12 2002

Status

approved