A347532 - OEIS

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

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OFFSET

1,3

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.

LINKS

Table of n, a(n) for n=1..56.

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

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)

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A208981 (number of nonpowers of 2).

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

Sequence in context: A023920 A214359 A198810 * A243911 A289660 A096306

Adjacent sequences: A347529 A347530 A347531 * A347533 A347534 A347535

KEYWORD

nonn

AUTHOR

Omar E. Pol, Sep 05 2021

STATUS

approved