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 A033044 Sums of distinct powers of 7. 7
 0, 1, 7, 8, 49, 50, 56, 57, 343, 344, 350, 351, 392, 393, 399, 400, 2401, 2402, 2408, 2409, 2450, 2451, 2457, 2458, 2744, 2745, 2751, 2752, 2793, 2794, 2800, 2801, 16807, 16808, 16814, 16815, 16856, 16857, 16863, 16864, 17150, 17151, 17157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Numbers without any base-7 digits greater than 1. a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - Philippe Deléham, Oct 17 2011 Note that this sequence has offset 1, in contrast to A000695 and all others among A033043-A033052. - M. F. Hasler, Feb 01 2016 LINKS T. D. Noe, Table of n, a(n) for n = 1..1024 FORMULA a(n) = Sum{d(i)*7^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} is the base 2 representation of n. a(n) = A097253(n)/6. a(2n) = 7*a(n), a(2n+1) = a(2n)+1. a(n+1) = Sum_k>=0 {A030308(n,k)*7^k}. - Philippe Deléham, Oct 17 2011 G.f.: (x/(1 - x))*Sum_{k>=0} 7^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017 MATHEMATICA t = Table[FromDigits[RealDigits[n, 2], 7], {n, 0, 100}] (* Clark Kimberling, Aug 03 2012 *) FromDigits[#, 7]&/@Tuples[{0, 1}, 6] (* Harvey P. Dale, Apr 30 2015 *) PROG (PARI) A033044(n, b=7)=subst(Pol(binary(n-1)), 'x, b) \\ M. F. Hasler, Feb 01 2016 (PARI) a(n)=fromdigits(binary(n), 7) \\ Charles R Greathouse IV, Jan 11 2017 CROSSREFS Cf. A000695, A005836, A033043-A033052, A037412. Row 7 of array A104257. Sequence in context: A119453 A047192 A270009 * A025630 A036566 A116554 Adjacent sequences:  A033041 A033042 A033043 * A033045 A033046 A033047 KEYWORD nonn,base,easy AUTHOR EXTENSIONS Extended by Ray Chandler, Aug 03 2004 Karol Bacik has pointed out that the first three formulas do not match the sequence. - N. J. A. Sloane, Oct 20 2012 STATUS approved

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Last modified October 18 00:17 EDT 2019. Contains 328135 sequences. (Running on oeis4.)