A082851 Partial sums of A082850.

1, 2, 4, 5, 6, 8, 11, 12, 13, 15, 16, 17, 19, 22, 26, 27, 28, 30, 31, 32, 34, 37, 38, 39, 41, 42, 43, 45, 48, 52, 57, 58, 59, 61, 62, 63, 65, 68, 69, 70, 72, 73, 74, 76, 79, 83, 84, 85, 87, 88, 89, 91, 94, 95, 96, 98, 99, 100, 102, 105, 109, 114, 120, 121, 122, 124, 125, 126

Offset

1,2

Comments

It seems that n/(2n-a(n)) is an integer for infinitely many values of n, see A082396.

Links

Paolo Xausa, Table of n, a(n) for n = 1..16383

Formula

Limit_{n->oo} a(n)/n = 2. Is (2-a(n)/n)*sqrt(n)*log(n) bounded?

Maple

A082850 := proc(n) option remember ; local m ; if n <= 3 then op(n, [1, 1, 2]) ; else m := ilog2(n+1) ; if n = 2^m -1 then m; else m := ilog2(n) ; return procname(n+1-2^m) ; end if ; end if; end proc:
A082851 := proc(n) add( A082850(i), i=1..n) ; end proc: seq(A082851(n), n=1..100) ; # R. J. Mathar, Nov 17 2009

Mathematica

A082850[n_] := A082850[n] = Module[{m}, If[n <= 3, {1, 1, 2}[[n]], m = Floor@Log2[n + 1]; If[n == 2^m - 1, m, m = Floor@Log2[n]; Return @ A082850[n + 1 - 2^m]]]];
Table[A082850[n], {n, 1, 68}] // Accumulate (* Jean-François Alcover, Dec 21 2023, after R. J. Mathar *)
Accumulate[Fold[Join[#, #, {#2}] &, {}, Range[7]]] (* Paolo Xausa, Jan 30 2025 *)

Crossrefs

Cf. A082850, A082396.

Sequence in context: A059916 A099747 A249053 * A091207 A284525 A353187

Adjacent sequences: A082848 A082849 A082850 * A082852 A082853 A082854

Keyword

nonn,easy,changed

Author

Benoit Cloitre, Apr 14 2003

Extensions

Minor edits by R. J. Mathar, Nov 17 2009

Status

approved