login
A347532
a(n) is the sum of the nonpowers of 2 in the 3x+1 sequence that starts at n.
2
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
1,3
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.
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).
Sequence in context: A023920 A214359 A198810 * A243911 A289660 A096306
KEYWORD
nonn
AUTHOR
Omar E. Pol, Sep 05 2021
STATUS
approved