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A062880
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Zero together with numbers which can be written as a sum of distinct odd powers of 2.
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11
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0, 2, 8, 10, 32, 34, 40, 42, 128, 130, 136, 138, 160, 162, 168, 170, 512, 514, 520, 522, 544, 546, 552, 554, 640, 642, 648, 650, 672, 674, 680, 682, 2048, 2050, 2056, 2058, 2080, 2082, 2088, 2090, 2176, 2178, 2184, 2186, 2208, 2210, 2216, 2218, 2560, 2562
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OFFSET
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0,2
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COMMENTS
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Binary expansion of n does not contain 1-bits at even positions.
Integers whose base-4 representation consists of only 0s and 2s.
a(n)=2 A000695(n). Every nonnegative even number is a unique sum of the form a(k)+2a(l); moreover, this sequence is unique with such property. [Vladimir Shevelev, Nov 07 2008]
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REFERENCES
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D. H. Bailey, J. M. Borwein, R. E. Crandall, and C. Pomerance, On the binary expansions of algebraic numbers, J. Theor. Nombres Bordeaux, 16 (2004), 487-518.
S. Eigen, A. Hajian, and S. Kalikow, Ergodic transformations and sequences of integers, Israel J. Math. 75 (1991), 119-128; Math. Rev. 1147294 (93c:28014).
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..10000
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MAPLE
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[seq(a(j), j=0..100)]; a := n -> add((floor(n/(2^i)) mod 2)*(2^((2*i)+1)), i=0..floor_log_2(n+1));
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PROG
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(Haskell)
a062880 n = a062880_list !! n
a062880_list = filter f [0..] where
f 0 = True
f x = (m == 0 || m == 2) && f x' where (x', m) = divMod x 4
-- Reinhard Zumkeller, Nov 20 2012
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CROSSREFS
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Except for first term, n such that A063694(n) = 0. Binary expansion is given in A062033.
Interpreted as Zeckendorf expansion: A062879. A062880[n] = 2*A000695[n]
Central diagonal of arrays A163357 and A163359.
Sequence in context: A209449 A002510 A102943 * A066707 A107227 A188539
Adjacent sequences: A062877 A062878 A062879 * A062881 A062882 A062883
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KEYWORD
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nonn,easy
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AUTHOR
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Antti Karttunen Jun 26 2001
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STATUS
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approved
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