A302338 a(n) = 3*n + 2^v(n) where v(n) denotes the 2-adic valuation of n.

4, 8, 10, 16, 16, 20, 22, 32, 28, 32, 34, 40, 40, 44, 46, 64, 52, 56, 58, 64, 64, 68, 70, 80, 76, 80, 82, 88, 88, 92, 94, 128, 100, 104, 106, 112, 112, 116, 118, 128, 124, 128, 130, 136, 136, 140, 142, 160, 148, 152, 154, 160, 160, 164, 166, 176, 172, 176, 178

Offset: 1

Author

Rémy Sigrist, Apr 28 2018

Keywords

• nonn
• easy

Comments

The sequence can be seen as a variant of the Collatz map (A006370) where we perform only tripling steps.

If the 3x+1 (or Collatz) conjecture is true, then for any n > 0, A006667(n) is the least k such that a^k(n) is a power of two (where a^k denotes the k-th iterate of the sequence).

Examples

			a(42) = 3*42 + 2^1 = 128.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A006667, A007814.

Programs

Magma

[3*n+2^Valuation(n, 2): n in [1..60]]; // Vincenzo Librandi, Apr 29 2018

Maple

seq(3*n+2^padic:-ordp(n,2), n=1..100); # Robert Israel, Apr 29 2018

Mathematica

Table[3 n + 2^IntegerExponent[n, 2], {n, 60}] (* Vincenzo Librandi, Apr 29 2018 *)

PARI

a(n) = 3*n + 2^valuation(n, 2)

Formula

a(n) = 3*n + 2^A007814(n).

a(2*n) = 2*a(n).

a(2*k + 1) = A006370(2*k + 1) for any k >= 0.