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A033043
Sums of distinct powers of 6.
12
0, 1, 6, 7, 36, 37, 42, 43, 216, 217, 222, 223, 252, 253, 258, 259, 1296, 1297, 1302, 1303, 1332, 1333, 1338, 1339, 1512, 1513, 1518, 1519, 1548, 1549, 1554, 1555, 7776, 7777, 7782, 7783, 7812, 7813, 7818, 7819, 7992, 7993, 7998, 7999, 8028, 8029, 8034
OFFSET
0,3
COMMENTS
Numbers without any base-6 digits greater than 1.
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. 6.
FORMULA
a(n) = Sum_{i=0..m} d(i)*6^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
a(n) = A097252(n)/5.
a(2n) = 6*a(n), a(2n+1) = a(2n)+1.
a(n) = Sum_{k>=0} A030308(n,k)*6^k. - Philippe Deléham, Oct 20 2011
G.f.: (1/(1 - x))*Sum_{k>=0} 6^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017
MATHEMATICA
t = Table[FromDigits[RealDigits[n, 2], 6], {n, 0, 100}] (* Clark Kimberling, Aug 02 2012 *)
FromDigits[#, 6]&/@Tuples[{0, 1}, 6] (* Harvey P. Dale, Mar 31 2016 *)
PROG
(PARI) A033043(n, b=6)=subst(Pol(binary(n)), 'x, b) \\ M. F. Hasler, Feb 01 2016
(PARI) a(n)=fromdigits(binary(n), 6) \\ 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 *= 6
end
r end; [a(n) for n in 0:46] |> println # Peter Luschny, Jan 03 2021
CROSSREFS
Row 6 of array A104257.
Sequence in context: A047190 A359530 A237711 * A037411 A025626 A175167
KEYWORD
nonn,base,easy
EXTENSIONS
Extended by Ray Chandler, Aug 03 2004
STATUS
approved