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

1,1

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).

Links

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

Index entries for sequences related to 3x+1 (or Collatz) problem

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A006370, A006667, A007814.

Sequence in context: A020169 A310999 A311000 * A311001 A311002 A082934

Adjacent sequences: A302335 A302336 A302337 * A302339 A302340 A302341

Keyword

nonn,easy

Author

Rémy Sigrist, Apr 28 2018

Status

approved