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A033045 Sums of distinct powers of 8. 8
0, 1, 8, 9, 64, 65, 72, 73, 512, 513, 520, 521, 576, 577, 584, 585, 4096, 4097, 4104, 4105, 4160, 4161, 4168, 4169, 4608, 4609, 4616, 4617, 4672, 4673, 4680, 4681, 32768, 32769, 32776, 32777, 32832, 32833, 32840, 32841, 33280, 33281, 33288 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Numbers without any base-8 digits greater than 1.

Every nonnegative n is a unique sum of the form a(p)+2a(q)+4a(r). This gives a one-to-one map of the set N_0 of all nonnegative integers to (N_0)^3. Furthermore, if, for a fixed positive integer m, to consider all sums of distinct powers of 2^m, then one can obtain a one-to-one map of the set N_0 to (N_0)^m. - Vladimir Shevelev, Nov 15 2008

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1023

FORMULA

a(n) = Sum_{i=0..m} d(i)*8^i, where Sum_{i=0..m} d(i)*2^i is the base 2 representation of n.

a(n) = A097254(n)/7.

a(2n) = 8*a(n), a(2n+1) = a(2n)+1.

a(n) = Sum_{k>=0} A030308(n,k)*8^k. - Philippe Deléham, Oct 19 2011

G.f.: (1/(1 - x))*Sum_{k>=0} 8^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

EXAMPLE

a(7)=72 because 72_10 = 110_8.

PROG

(PARI) A033045(n, b=8)=subst(Pol(binary(n)), 'x, b) \\ M. F. Hasler, Feb 01 2016

CROSSREFS

Cf. A000695, A005836, A033043-A033052.

Row 8 of array A104257.

Sequence in context: A121330 A152189 A042873 * A025633 A249697 A038287

Adjacent sequences:  A033042 A033043 A033044 * A033046 A033047 A033048

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Patrick De Geest, Dec 23 2000

STATUS

approved

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Last modified October 20 19:44 EDT 2018. Contains 316401 sequences. (Running on oeis4.)