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 A033042 Sums of distinct powers of 5. 36
 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 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 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 EXTENSIONS Extended by Ray Chandler, Aug 03 2004 STATUS approved

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Last modified August 18 00:28 EDT 2018. Contains 313817 sequences. (Running on oeis4.)