A137604 Consider the sequence: b(0) = n, and for k >= 1, b(k) = b(k-1)/2 if b(k-1) is even, otherwise b(k) = n - (b(k-1)+1)/2. Then a(n) = (Sum_{0<=k<=m} b(k)) - 1 for n > 1, where m is the smallest index such that b(m) = 1; a(1) = 1.

1, 2, 3, 6, 7, 15, 21, 14, 15, 45, 30, 66, 63, 61, 105, 30, 31, 102, 171, 114, 93, 63, 134, 276, 258, 88, 351, 270, 105, 435, 465, 62, 63, 561, 374, 630, 126, 374, 570, 780, 547, 861, 126, 602, 204, 246, 196, 846, 537, 361, 1275, 1326, 264, 1431, 483, 990, 315

Offset: 1

Author

Yasutoshi Kohmoto, Apr 23 2008

Keywords

• nonn

Examples

			a(6) = 6 + 3 + 4 + 2 + 1 - 1 = 15.
		

Crossrefs

Cf. A096259, A137605.

Programs

Mathematica

f[1] = 1; f[n_] := Block[{lst = {n}, a}, While[a = lst[[ -1]]; a != 1, If[EvenQ@ a, AppendTo[lst, a/2], AppendTo[lst, lst[[1]] - (a + 1)/2]]]; Plus @@ lst - 1]; Array[f, 58] (* Robert G. Wilson v, May 15 2008 *)

Extensions

More terms from Robert G. Wilson v, May 15 2008