A074938 Odd numbers such that base 3 representation contains no 2.

1, 3, 9, 13, 27, 31, 37, 39, 81, 85, 91, 93, 109, 111, 117, 121, 243, 247, 253, 255, 271, 273, 279, 283, 325, 327, 333, 337, 351, 355, 361, 363, 729, 733, 739, 741, 757, 759, 765, 769, 811, 813, 819, 823, 837, 841, 847, 849, 973, 975, 981, 985, 999, 1003, 1009

Offset

0,2

Comments

Odd numbers in A005836.

Numbers m such that coefficient of x^m equals -1 in Product_{k>=0} 1-x^(3^k).

Numbers k such that binomial(2k, k) == 2 (mod 3).

Sum of an odd number of distinct powers of 3. - Emeric Deutsch, Dec 03 2003

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Emeric Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, arXiv:math/0407326 [math.CO], 2004; J. Num. Theory 117 (2006), 191-215.

Formula

a(n) (mod 3) = A010059(n).

((a(n)-1)/2) (mod 3) = A010060(n) = (1/2)*{binomial(2*a(n)+1, a(n)) (mod 3)}.

Mathematica

Select[Range[1, 1111, 2], Count[IntegerDigits[#, 3], 2]==0&] (* Harvey P. Dale, Dec 19, 2010 *)

Crossrefs

Intersection of A005408 and A005836.

Cf. A006996, A074939.

Sequence in context: A079994 A303964 A124825 * A057260 A107364 A014861

Adjacent sequences: A074935 A074936 A074937 * A074939 A074940 A074941

Keyword

easy,nonn

Author

Benoit Cloitre, Oct 04 2002; Nov 15 2003

Status

approved