



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, 10, 9, 12, 11, 14, 10, 12, 11, 16, 13, 15, 12, 14, 9, 10, 9, 14, 12, 15, 13, 16, 11, 12, 10, 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
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OFFSET

1,2


COMMENTS

Proposed name: Nfusc.
Each number n>0 appears in this sequence exactly n times.
From Yosu Yurramendi, Apr 08 2019: (Start)
The terms (n>0) may be written as a leftjustified array with rows of length 2^m:
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, 10, 9, 12, 11, 14, 10, 12, 11, 16, 13, 15, 12, 14, 9, 10, 9, ...
...
as well as rightjustified fashion:
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,
... 14, 9, 10, 9, 14, 12, 15, 13, 16, 11, 12, 10, 14, 11, 12, 9, 10, 6,
From these two dispositions interesting properties can be induced (see FORMULA section)
(End)


LINKS

I. V. Serov, Table of n, a(n) for n = 1..8192


FORMULA

a(1) = 1; for n>1: a(n) = (A002487(n1) + A002487(n) + A002487(n+1))/2.
a(n) = A007306(n)  A288002(n).
From Yosu Yurramendi, Apr 08 2019: (Start)
For m >= 0, 0 <= k < 2^m, a(2^(m+1)+k)  a(2^m+k) = a(k). a(0) = 1 is needed.
For m >= 0, 0 <= k < 2^m, a(2^(m+1)1k)  a(2^(m)1k) = a(k).
(End)


MATHEMATICA

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 JeanFrançois Alcover at A002487 *)


CROSSREFS

Cf. A001511, A002487, A007306, A288002.
Sequence in context: A319856 A100197 A057022 * A087504 A067539 A166312
Adjacent sequences: A287893 A287894 A287895 * A287897 A287898 A287899


KEYWORD

nonn


AUTHOR

I. V. Serov, Jun 02 2017


STATUS

approved



