

A062880


Zero together with numbers which can be written as a sum of distinct odd powers of 2.


16



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

0,2


COMMENTS

Binary expansion of n does not contain 1bits at even positions.
Integers whose base4 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]
Also numbers such that the digital sum base 2 and the digital sum base 4 are in a ratio of 2:4.  Michel Marcus, Sep 23 2013


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
D. H. Bailey, J. M. Borwein, R. E. Crandall, and C. Pomerance, On the binary expansions of algebraic numbers, J. Théor. Nombres Bordeaux, 16 (2004), 487518.
S. Eigen, A. Hajian, and S. Kalikow, Ergodic transformations and sequences of integers, Israel J. Math. 75 (1991), 119128; Math. Rev. 1147294 (93c:28014).


FORMULA

From Robert Israel, Apr 10 2018: (Start)
a(2*n) = 4*a(n).
a(2*n+1) = 4*a(n)+2.
G.f. g(x) satisfies: g(x) = 4*(1+x)*g(x^2)+2*x/(1x^2). (End)


MAPLE

[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));


MATHEMATICA

b[n_] := BitAnd[n, Sum[2^k, {k, 0, Log[2, n] // Floor, 2}]]; Select[Range[ 0, 10^4], b[#] == 0&] (* JeanFrançois Alcover, Feb 28 2016 *)


PROG

(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


CROSSREFS

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: A002510 A247592 A102943 * A066707 A107227 A188539
Adjacent sequences: A062877 A062878 A062879 * A062881 A062882 A062883


KEYWORD

nonn,easy


AUTHOR

Antti Karttunen, Jun 26 2001


STATUS

approved



