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a(n) = A002487(n)*A001511(n).
10

%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