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

Author

Benoit Cloitre, Apr 14 2003

Keywords

• nonn
• easy

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

Crossrefs

Cf. A082850, A082396.

Programs

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 *)

Formula

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

Extensions

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