A347532 a(n) is the sum of the nonpowers of 2 in the 3x+1 sequence that starts at n.

0, 0, 18, 0, 5, 24, 257, 0, 308, 15, 228, 36, 88, 271, 663, 0, 183, 326, 488, 35, 21, 250, 602, 60, 627, 114, 101409, 299, 411, 693, 101073, 0, 810, 217, 509, 362, 504, 526, 2313, 75, 101300, 63, 1307, 294, 466, 648, 100948, 108, 775, 677, 1099, 166, 368, 101463, 102285, 355

Offset: 1

Author

Omar E. Pol, Sep 05 2021

Keywords

• nonn

Comments

a(n) is the sum of the nonpowers of 2 in the n-th row of A347270.

a(n) = 0 if and only if n is a power of 2.

Examples

			For n = 6 the 3x+1 sequence starting at 6 is 6, 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, ... Only the first four terms are nonpowers of 2. The sum of them is 6 + 3 + 10 + 5 = 24, so a(6) = 24.
		

Links

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

Crossrefs

Cf. A208981 (number of nonpowers of 2).

Cf. A000079, A006370, A033493, A033495, A057716, A135282, A232503, A347270, A347519.

Programs

Maple

a:= proc(n) option remember; `if`(n=2^ilog2(n), 0,
      n+a(`if`(n::odd, 3*n+1, n/2)))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 05 2021

Mathematica

a[n_] := Plus @@ Select[NestWhileList[If[OddQ[#], 3*# + 1, #/2] &, n, # > 1 &], # != 2^IntegerExponent[#, 2] &]; Array[a, 50] (* Amiram Eldar, Sep 06 2021 *)

Formula

From Alois P. Heinz, Sep 05 2021: (Start)

a(n) = A033493(n) - 2 * A232503(n) + 1.

a(n) = A033493(n) - 2^(A135282(n)+1) + 1. (End)