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A033042 Sums of distinct powers of 5. 35
0, 1, 5, 6, 25, 26, 30, 31, 125, 126, 130, 131, 150, 151, 155, 156, 625, 626, 630, 631, 650, 651, 655, 656, 750, 751, 755, 756, 775, 776, 780, 781, 3125, 3126, 3130, 3131, 3150, 3151, 3155, 3156, 3250, 3251, 3255, 3256, 3275, 3276, 3280, 3281, 3750, 3751 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Numbers without any base-5 digits larger than 1.

a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - Philippe Deléham, Oct 17 2011

LINKS

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

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

K. Dilcher and L. Ericksen, Hyperbinary expansions and Stern polynomials, Elec. J. Combin, 22, 2015, #P2.24.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

FORMULA

a(n) = Sum_{i=0..m} d(i)*5^i, where Sum_{i=0..m} d(i)*2^i is the base 2 representation of n.

n such that the coefficient of x^n is > 0 in Product_{k>=0} (1+x^(5^k)). - Benoit Cloitre, Jul 29 2003

a(n) = A097251(n)/4.

a(2n) = 5*a(n), a(2n+1) = a(2n)+1.

a(n) = Sum_{k>=0} A030308(n,k)*5^k. - Philippe Deléham, Oct 17 2011

liminf a(n)/n^(log(5)/log(2)) = 1/4 and limsup a(n)/n^(log(5)/log(2)) = 1. - Gheorghe Coserea, Sep 15 2015

MAPLE

a:= proc(n) local m, r, b; m, r, b:= n, 0, 1;

      while m>0 do r:= r+b*irem(m, 2, 'm'); b:= b*5 od; r

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, Mar 16 2013

MATHEMATICA

t = Table[FromDigits[RealDigits[n, 2], 5], {n, 1, 100}]

(* Clark Kimberling, Aug 02 2012 *)

PROG

(PARI) a(n) = subst(Pol(binary(n)), 'x, 5);

vector(50, i, a(i-1))  \\ Gheorghe Coserea, Sep 15 2015

(PARI) a(n)=fromdigits(binary(n), 5) \\ Charles R Greathouse IV, Jan 11 2017

CROSSREFS

For generating functions Prod_{k>=0} (1+a*x^(b^k)) for the following values of (a,b) see: (1,2) A000012 and A000027, (1,3) A039966 and A005836, (1,4) A151666 and A000695, (1,5) A151667 and A033042, (2,2) A001316, (2,3) A151668, (2,4) A151669, (2,5) A151670, (3,2) A048883, (3,3) A117940, (3,4) A151665, (3,5) A151671, (4,2) A102376, (4,3) A151672, (4,4) A151673, (4,5) A151674.

Cf. A000695, A005836, A033043-A033052.

Row 5 of array A104257.

Sequence in context: A166591 A160529 A039572 * A039594 A137080 A025622

Adjacent sequences:  A033039 A033040 A033041 * A033043 A033044 A033045

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Extended by Ray Chandler, Aug 03 2004

STATUS

approved

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Last modified April 28 23:30 EDT 2017. Contains 285604 sequences.