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A033048 Sums of distinct powers of 12. 6
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 (list; graph; refs; listen; history; text; internal format)
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

Eric Weisstein's World of Mathematics, Duodecimal

Wikipedia, Duodecimal

FORMULA

a(n) = Sum{d(i)*12^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} 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

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: A243361 A037278 A164852 * 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

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Last modified February 18 05:48 EST 2018. Contains 299298 sequences. (Running on oeis4.)