A102421 To get a(n), start with 2n+1, multiply by 3 and add 1 and divide out any power of 2; then multiply by 3 and subtract 1 and divide out any power of 2.

1, 7, 1, 1, 5, 25, 7, 17, 19, 43, 1, 13, 7, 61, 1, 35, 37, 79, 5, 11, 23, 97, 25, 53, 55, 115, 7, 31, 1, 133, 17, 71, 73, 151, 19, 5, 41, 169, 43, 89, 91, 187, 1, 49, 25, 205, 13, 107, 109, 223, 7, 29, 59, 241, 61, 125, 127, 259, 1, 67, 17, 277, 35, 143, 145, 295, 37, 19, 77, 313

Offset: 0

Author

N. J. A. Sloane, based on email from Dan Asimov (dasimov(AT)earthlink.net), Sep 15 2006

Keywords

• nonn

Comments

"Start with 2n+1, multiply by 3 and add 1 and divide out any power of 2;" is "equivalent to Start with 3n+2, divide out any power of 2;" - David A. Corneth, Aug 22 2020

Examples

			n=1, 2n+1 = 3 -> 10 -> 5; 5 -> 14 ->7 = a(1).
n=17, 2*n+1 = 35 -> 106 ->53; 53 -> 158 -> 79 = a(17).
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A000265, A102423.

Programs

Maple

A102421 :=proc(n) local j; j:=3*n+1; while j mod 2 = 0 do j:=j/2; od: j:=3*j-1; while j mod 2 = 0 do j:=j/2; od: j; end proc;

Mathematica

nextx[x_Integer] := Block[{ a = x}, a = 3a + 1; While[EvenQ@a, a /= 2]; a = 3a - 1; While[EvenQ@a, a /= 2]; a]; Table[ nextx[2n + 1], {n, 0, 69}] (* Robert G. Wilson v Sep 20 2006 *)

PARI

a(n) = {n = 3*n + 2; n>>=valuation(n, 2); n = 3*n - 1; n >> valuation(n, 2)} \\ David A. Corneth, Aug 22 2020

Formula

a(n) = A337349(2*n+1). - R. J. Mathar, Aug 24 2020

Extensions

Moved comments to A337349. - R. J. Mathar, Aug 24 2020