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

Author

Pierre CAMI, Sep 20 2019

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

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

Crossrefs

Intersection of A005408 and A225570.

Programs

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

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.

Extensions

More terms from Jinyuan Wang, Sep 21 2019