A129343 a(2n) = a(n), a(2n+1) = 4n+1.

0, 1, 1, 5, 1, 9, 5, 13, 1, 17, 9, 21, 5, 25, 13, 29, 1, 33, 17, 37, 9, 41, 21, 45, 5, 49, 25, 53, 13, 57, 29, 61, 1, 65, 33, 69, 17, 73, 37, 77, 9, 81, 41, 85, 21, 89, 45, 93, 5, 97, 49, 101, 25, 105, 53, 109, 13, 113, 57, 117, 29, 121, 61, 125, 1, 129, 65, 133, 33, 137

Offset

0,4

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(n) = 2*A000265(n) - 1, for n >= 1.

a(n) = 2*n/2^A007814(n) - 1, for n >= 1.

Sum_{k=0..n} a(k) = (2/3) * n^2 + O(n). - Amiram Eldar, Mar 17 2025

Mathematica

a[n_] := 2 * n/ 2^IntegerExponent[n, 2] - 1; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Mar 17 2025 *)

Prog

(PARI) a(n) = if(n == 0, 0, 2*n >> valuation(n, 2) - 1); \\ Amiram Eldar, Mar 17 2025

Crossrefs

Cf. A000265, A007814.

Sequence in context: A199736 A207873 A198671 * A342634 A010482 A135856

Adjacent sequences: A129340 A129341 A129342 * A129344 A129345 A129346

Keyword

nonn,easy

Author

Ralf Stephan, May 28 2007

Status

approved