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A033048
Sums of distinct powers of 12.
7
0, 1, 12, 13, 144, 145, 156, 157, 1728, 1729, 1740, 1741, 1872, 1873, 1884, 1885, 20736, 20737, 20748, 20749, 20880, 20881, 20892, 20893, 22464, 22465, 22476, 22477, 22608, 22609, 22620, 22621, 248832, 248833, 248844, 248845, 248976
OFFSET
0,3
COMMENTS
Numbers without any base-12 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. 45.
Eric Weisstein's World of Mathematics, Duodecimal
Wikipedia, Duodecimal
FORMULA
a(n) = Sum_{i=0..m} d(i)*12^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
a(n) = A097258(n)/11.
a(2n) = 12*a(n), a(2n+1) = a(2n)+1.
a(n) = Sum_{k>=0} A030308(n,k)*b(k) with b(k) = 12^k = A001021(k). - Philippe Deléham, Oct 19 2011
G.f.: (1/(1 - x))*Sum_{k>=0} 12^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017
MATHEMATICA
With[{k = 12}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* Michael De Vlieger, Oct 28 2022 *)
PROG
(PARI) {maxn=37;
for(vv=0, maxn,
bvv=binary(vv);
ll=length(bvv); texp=0; btod=0;
forstep(i=ll, 1, -1, btod=btod+bvv[i]*12^texp; texp++);
print1(btod, ", "))}
\\ Douglas Latimer, Apr 16 2012
(PARI) a(n)=fromdigits(binary(n), 12) \\ Charles R Greathouse IV, Jan 11 2017
(Haskell)
import Data.List (unfoldr)
a033048 n = a033048_list !! (n-1)
a033048_list = filter (all (< 2) . unfoldr (\x ->
if x == 0 then Nothing else Just $ swap $ divMod x 12)) [1..]
-- Reinhard Zumkeller, Apr 17 2011
CROSSREFS
Subsequence of A102487.
Row 11 of array A104257.
Sequence in context: A037278 A164852 A362113 * A108771 A041308 A260387
KEYWORD
nonn,base,easy
EXTENSIONS
Extended by Ray Chandler, Aug 03 2004
STATUS
approved