A033048 Sums of distinct powers of 12.

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

T. D. Noe, Table of n, a(n) for n = 0..1023

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.

Cf. A000695, A005836, A033042-A033052.

Row 11 of array A104257.

Sequence in context: A037278 A164852 A362113 * A108771 A041308 A260387

Adjacent sequences: A033045 A033046 A033047 * A033049 A033050 A033051

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

Extended by Ray Chandler, Aug 03 2004

Status

approved