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Search: id:A048645
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| A048645 |
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Integers with one or two 1-bits in their binary expansion. |
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+0
14
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| 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 20, 24, 32, 33, 34, 36, 40, 48, 64, 65, 66, 68, 72, 80, 96, 128, 129, 130, 132, 136, 144, 160, 192, 256, 257, 258, 260, 264, 272, 288, 320, 384, 512, 513, 514, 516, 520, 528, 544, 576, 640, 768, 1024, 1025, 1026, 1028, 1032
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Apart from initial 1, sums of two not necessarily distinct powers of 2.
4 does not divide C(2s-1,s) (= A001700[ s ]) if and only if s=a(n).
Possible number of sides of a regular polygon such that there exists a triangulation where each triangle is isosceles. - Sen-Peng Eu (speu(AT)nuk.edu.tw), May 07 2008
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REFERENCES
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USA Mathematical Olympiad, 2008, Problem 4.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(0) = 1, a(n) = (2^(trinv(n-1)-1) + 2^((n-1)-((trinv(n-1)*(trinv(n-1)-1))/2))) i.e. 2^A003056(n)+2^A002262(n-1) (the latter sequence contains the definition of trinv).
Let Theta = Sum_{k >= 0} x^(2^k). Then Sum_{n>=1} x^a(n) = (Theta^2 + Theta + x)/2. - N. J. A. Sloane, Jun 23 2009
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MAPLE
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lincom:=proc(a, b, n) local i, j, s, m; s:={}; for i from 0 to n do for j from 0 to n do m:=a^i+b^j; if m<=n then s:={op(s), m} fi od; od; lprint(sort([op(s)])); end: lincom(2, 2, 1000); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 24 2007
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CROSSREFS
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Cf. A018900, A048623, A046097.
Sequence in context: A018412 A061945 A029509 this_sequence A093863 A091902 A067698
Adjacent sequences: A048642 A048643 A048644 this_sequence A048646 A048647 A048648
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Antti Karttunen, Jul 14 1999
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