

A165275


Number of oddpower summands in base 2 representations.


1



1, 4, 2, 5, 3, 10, 16, 6, 11, 42, 17, 7, 14, 43, 170, 20, 8, 15, 46, 171, 682, 21, 9, 26, 47, 174, 683, 2730, 64, 12, 27, 58, 175, 686, 2731, 10922, 65, 13, 30, 59, 186, 687, 2734, 10923, 43690, 68, 18, 31, 62, 187, 698, 2735, 10926, 43691
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OFFSET

1,2


COMMENTS

For n>=0, row n is the ordered sequence of positive integers m such
that the number of odd powers of 2 in the base 2 representation of m
is n. Every positive integer occurs exactly once in the array, so that
as a sequence it is a permutation of the positive integers. For even
powers, see A165274. For the number of even powers of 2 in the
base 2 representation of n, see A139351; for odd, see A139352.
Essentially, (Row 0)=A000695, (Column 1)=A020988, also possibly
(Column 2)=A007583.
It appears that, for n>=3, a(t(n))=4*a(t(n1))+2, where t(n) is the nth triangular number t(n)=n(n+1)/2 (A000217). [From John W. Layman, Sep 15 2009]


LINKS

Table of n, a(n) for n=1..54.


EXAMPLE

Northwest corner:
1....4....5...16...17...20...21...64
2....3....6....7....8....9...12...13
10..11...14...26...27...30...31...34
42..43...46...47...58...59...62...63
Examples:
20 = 16 + 4 = 2^4 + 2^2, so that 20 is in row 0.
13 = 8 + 4 + 1 = 2^3 + 2^2 + 2^0, so that 13 is in row 1.


CROSSREFS

Cf. A139351, A139352, A165274, A165276, A165277, A165278, A165279.
A000217 [From John W. Layman, Sep 15 2009]
Sequence in context: A219159 A213928 A065189 * A163363 A065258 A049259
Adjacent sequences: A165272 A165273 A165274 * A165276 A165277 A165278


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Sep 12 2009


EXTENSIONS

a(27) corrected and a(28)a(54) added by John W. Layman, Sep 15 2009


STATUS

approved



