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A033047
Sums of distinct powers of 11.
5
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
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
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.
FORMULA
a(n) = Sum_{i=0..m} d(i)*11^i, where Sum_{i=0..m} d(i)*2^i 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
MATHEMATICA
With[{k = 11}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* Michael De Vlieger, Oct 28 2022 *)
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
Row 10 of array A104257.
Sequence in context: A296447 A110380 A164854 * A094624 A108218 A038326
KEYWORD
nonn,base,easy
EXTENSIONS
Extended by Ray Chandler, Aug 03 2004
STATUS
approved