A327638 a(0)=1, a(1)=5; for n > 2, a(n) is the smallest odd number j not divisible by 3 such that (3*j+1)/2^k = a(n-1) for some k.

1, 5, 13, 17, 11, 7, 37, 49, 65, 43, 229, 305, 203, 541, 721, 961, 5125, 6833, 4555, 6073, 32389, 172741, 230321, 153547, 818917, 4367557, 5823409, 7764545, 5176363, 6901817, 18404845, 98159173, 523515589, 2792083141, 3722777521, 19854813445, 105892338373

Offset

0,2

Comments

Also a reverse Collatz sequence with odd numbers. - Paul Conradi, Oct 23 2020

Odd numbers in A225570. - Michel Marcus, Oct 24 2020

Links

Michel Marcus, Table of n, a(n) for n = 0..295

Formula

If a(n-1) == 1 (mod 3) then a(n) = (4*a(n-1)-1)/3 or (16*a(n-1)-1)/3, whichever value is not divisible by 3.

If a(n-1) == -1 (mod 3) then a(n) = (2*a(n-1)-1)/3 or a(n)=(8*a(n-1)-1)/3, whichever value is not divisible by 3.

Example

a(0)=1, a(1)=5 by definition, then a(2) = (2*5-1)/3 or (8*5-1)/3; as (2*5-1)/3 is divisible by 3, a(2) = (8*5-1)/3 = 13.

Prog

(PARI) lista(nn) = {print1(1, ", ", 5); x = 5; for (n = 2, nn, if(x%3 == 1, x = (4*x-1)/3, x = (2*x-1)/3); if(x%3 == 0, x = 4*x + 1); print1(", ",  x)); } \\ Jinyuan Wang, Sep 21 2019

Crossrefs

Intersection of A005408 and A225570.

Sequence in context: A158334 A282747 A088908 * A092218 A049092 A103666

Adjacent sequences: A327635 A327636 A327637 * A327639 A327640 A327641

Keyword

nonn

Author

Pierre CAMI, Sep 20 2019

Extensions

More terms from Jinyuan Wang, Sep 21 2019

Status

approved