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A033044
Sums of distinct powers of 7.
8
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
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
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)*7^i, where Sum_{i=0..m} d(i)*2^i 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
Row 7 of array A104257.
Sequence in context: A047192 A342611 A270009 * A025630 A036566 A116554
KEYWORD
nonn,base,easy
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