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A033047 Sums of distinct powers of 11. 4
0, 1, 11, 12, 121, 122, 132, 133, 1331, 1332, 1342, 1343, 1452, 1453, 1463, 1464, 14641, 14642, 14652, 14653, 14762, 14763, 14773, 14774, 15972, 15973, 15983, 15984, 16093, 16094, 16104, 16105, 161051, 161052, 161062, 161063, 161172 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Numbers without any base-11 digits greater than 1.

a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - Philippe Deléham, Oct 17 2011

LINKS

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

FORMULA

a(n) = Sum{d(i)*11^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} is the base 2 representation of n.

a(n) = A097257(n)/10.

a(2n) = 11*a(n), a(2n+1) = a(2n)+1.

a(n) = Sum_{k>=0} {A030308(n,k)*11^k. - Philippe Deléham, Oct 17 2011

G.f.: (1/(1 - x))*Sum_{k>=0} 11^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

PROG

(PARI) {for(vv=0, 35,

bvv=binary(vv);

texp=0; btb=0;

forstep(i=length(bvv), 1, -1, btb=btb+bvv[i]*11^texp; texp++);

print1(btb, ", "))} \\ Douglas Latimer, May 12 2012

(PARI) a(n)=fromdigits(binary(n), 11) \\ Charles R Greathouse IV, Jan 11 2017

CROSSREFS

Cf. A000695, A005836, A033042-A033052.

Row 10 of array A104257.

Sequence in context: A296447 A110380 A164854 * A094624 A108218 A038326

Adjacent sequences:  A033044 A033045 A033046 * A033048 A033049 A033050

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Extended by Ray Chandler, Aug 03 2004

STATUS

approved

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Last modified October 16 14:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)