

A297405


Binary "cubes"; numbers whose binary representation consists of three consecutive identical blocks.


2



7, 42, 63, 292, 365, 438, 511, 2184, 2457, 2730, 3003, 3276, 3549, 3822, 4095, 16912, 17969, 19026, 20083, 21140, 22197, 23254, 24311, 25368, 26425, 27482, 28539, 29596, 30653, 31710, 32767, 133152, 137313, 141474, 145635, 149796, 153957, 158118, 162279, 166440, 170601, 174762, 178923, 183084, 187245
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OFFSET

1,1


COMMENTS

Alternatively, numbers of the form k*(4^n + 2^n + 1), where 2^{n1} <= k < 2^n .


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Daniel M. Kane, Carlo Sanna, Jeffrey Shallit, Waring's Theorem for Binary Powers, arXiv:1801.04483 [math.NT], 2018.
Index entries for sequences related to binary expansion of n


FORMULA

a(n) = n * (1+2^p+4^p) with p = 1 + floor(log_2(n)).  Alois P. Heinz, Dec 29 2017
G.f.: (7*x + Sum_{n>=1} (4^n+3*8^n+(2^n+2*4^n3*8^n)*x)*x^(2^n))/(1x)^2.  Robert Israel, Dec 31 2017


EXAMPLE

42 in base 2 is 101010, which consists of three copies of the block "10".


MAPLE

a:= n> (p> n*(1+2^p+4^p))(1+ilog2(n)):
seq(a(n), n=1..50); # Alois P. Heinz, Dec 29 2017


CROSSREFS

Cf. A020330, which is the corresponding sequence for squares.
Subsequence of A121016.
Sequence in context: A188066 A225327 A102532 * A044109 A195320 A110451
Adjacent sequences: A297402 A297403 A297404 * A297406 A297407 A297408


KEYWORD

nonn,base


AUTHOR

Jeffrey Shallit, Dec 29 2017


STATUS

approved



