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
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
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