%I #44 Sep 07 2023 16:09:44
%S 1,2,2,3,3,4,3,4,4,6,5,6,5,6,4,5,5,8,7,9,8,10,7,8,7,10,8,9,7,8,5,6,6,
%T 10,9,12,11,14,10,12,11,16,13,15,12,14,9,10,9,14,12,15,13,16,11,12,10,
%U 14,11,12,9,10,6,7,7,12,11,15,14,18,13,16,15,22,18,21,17,20,13,15,14,22,19,24,21,26,18,20,17
%N a(n) = A002487(n)*A001511(n).
%C Proposed name: N-fusc.
%C Each number n>0 appears in this sequence exactly n times.
%C From _Yosu Yurramendi_, Apr 08 2019: (Start)
%C The terms (n>0) may be written as a left-justified array with rows of length 2^m:
%C 1,
%C 2, 2,
%C 3, 3, 4, 3,
%C 4, 4, 6, 5, 6, 5, 6, 4,
%C 5, 5, 8, 7, 9, 8, 10, 7, 8, 7, 10, 8, 9, 7, 8, 5,
%C 6, 6, 10, 9, 12, 11, 14, 10, 12, 11, 16, 13, 15, 12, 14, 9, 10, 9, ...
%C ...
%C as well as right-justified fashion:
%C 1,
%C 2, 2,
%C 3, 3, 4, 3,
%C 4, 4, 6, 5, 6, 5, 6, 4,
%C 5, 5, 8, 7, 9, 8, 10, 7, 8, 7, 10, 8, 9, 7, 8, 5,
%C ... 14, 9, 10, 9, 14, 12, 15, 13, 16, 11, 12, 10, 14, 11, 12, 9, 10, 6,
%C From these two dispositions interesting properties can be induced (see FORMULA section)
%C (End)
%H I. V. Serov, <a href="/A287896/b287896.txt">Table of n, a(n) for n = 1..8192</a>
%F a(1) = 1; for n>1: a(n) = (A002487(n-1) + A002487(n) + A002487(n+1))/2.
%F a(n) = A007306(n) - A288002(n).
%F From _Yosu Yurramendi_, Apr 08 2019: (Start)
%F For m >= 0, 0 <= k < 2^m, a(2^(m+1)+k) - a(2^m+k) = a(k). a(0) = 1 is needed.
%F For m >= 0, 0 <= k < 2^m, a(2^(m+1)-1-k) - a(2^(m)-1-k) = a(k).
%F (End)
%t Table[Block[{a = 1, b = 0, m = n}, While[m > 0, If[OddQ@ m, b = a + b, a = a + b]; m = Floor[m/2]]; b] IntegerExponent[2 n, 2], {n, 89}] (* _Michael De Vlieger_, Jun 14 2017, after _Jean-François Alcover_ at A002487 *)
%o (Python)
%o from functools import reduce
%o def A287896(n): return (n&-n).bit_length()*sum(reduce(lambda x,y:(x[0],x[0]+x[1]) if int(y) else (x[0]+x[1],x[1]),bin(n)[-1:2:-1],(1,0))) # _Chai Wah Wu_, Jul 14 2022
%Y Cf. A001511, A002487, A007306, A288002.
%K nonn
%O 1,2
%A _I. V. Serov_, Jun 02 2017