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%I #15 Dec 21 2023 07:43:07
%S 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,
%T 42,43,45,48,52,57,58,59,61,62,63,65,68,69,70,72,73,74,76,79,83,84,85,
%U 87,88,89,91,94,95,96,98,99,100,102,105,109,114,120,121,122,124,125,126
%N Partial sums of A082850.
%C It seems that n/(2n-a(n)) is an integer for infinitely many values of n, see A082396.
%F Limit_{n->oo} a(n)/n = 2. Is (2-a(n)/n)*sqrt(n)*log(n) bounded?
%p 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:
%p A082851 := proc(n) add( A082850(i),i=1..n) ; end proc: seq(A082851(n),n=1..100) ; # _R. J. Mathar_, Nov 17 2009
%t 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]]]];
%t Table[A082850[n], {n, 1, 68}] // Accumulate (* _Jean-François Alcover_, Dec 21 2023, after _R. J. Mathar_ *)
%Y Cf. A082850, A082396.
%K nonn,easy
%O 1,2
%A _Benoit Cloitre_, Apr 14 2003
%E Minor edits by _R. J. Mathar_, Nov 17 2009
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