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A074938 Odd numbers such that base 3 representation contains no 2. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Odd numbers in A005836 n; n such that binomial(2n,n)==2 (mod 3)

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

LINKS

Table of n, a(n) for n=0..54.

E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, 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)}; n such that coefficient of x^n equals -1 in prod(k>=0, 1-x^(3^k))

MATHEMATICA

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

CROSSREFS

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

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Last modified March 8 20:14 EST 2021. Contains 341953 sequences. (Running on oeis4.)