login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033042 Sums of distinct powers of 5. 38
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
Values of k where A008977(k) does not end with 0. - Henry Bottomley, Nov 09 2022
LINKS
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
K. Dilcher and L. Ericksen, Hyperbinary expansions and Stern polynomials, Elec. J. Combin, 22, 2015, #P2.24.
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 45.
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.
Numbers j such that the coefficient of x^j 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
G.f.: (1/(1 - x))*Sum_{k>=0} 5^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017
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 *)
FromDigits[#, 5]&/@Tuples[{0, 1}, 7] (* Harvey P. Dale, May 22 2018 *)
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
(Julia)
function a(n)
m, r, b = n, 0, 1
while m > 0
m, q = divrem(m, 2)
r += b * q
b *= 5
end
r end; [a(n) for n in 0:49] |> println # Peter Luschny, Jan 03 2021
CROSSREFS
For generating functions Product_{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.
Row 5 of array A104257.
Sequence in context: A342610 A160529 A039572 * A039594 A137080 A025622
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
Extended by Ray Chandler, Aug 03 2004
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:52 EDT 2024. Contains 370953 sequences. (Running on oeis4.)