A074939 Even numbers such that base 3 representation contains no 2.

0, 4, 10, 12, 28, 30, 36, 40, 82, 84, 90, 94, 108, 112, 118, 120, 244, 246, 252, 256, 270, 274, 280, 282, 324, 328, 334, 336, 352, 354, 360, 364, 730, 732, 738, 742, 756, 760, 766, 768, 810, 814, 820, 822, 838, 840, 846, 850, 972, 976, 982, 984, 1000, 1002

Offset

0,2

Comments

Even numbers in A005836; n such that binomial(2n,n) == 1 (mod 3).

Sum of an even 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.

Emeric Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, J. Num. Theory 117 (2006), 191-215.

Formula

a(n) = A083094(n)/2; a(n) mod 3 = A010060(n); n such that coefficient of x^n equals 1 in Product_{k>=0} (1 - x^(3^k)).

a(n) + A074938(n) = A055246(n+1). - Philippe Deléham, Jul 10 2005

Mathematica

Select[2*Range[0, 600], DigitCount[#, 3, 2]==0&] (* Harvey P. Dale, Dec 10 2016 *)
Select[FromDigits[#, 3]&/@Tuples[{0, 1}, 7], EvenQ] (* Harvey P. Dale, Nov 25 2025 *)

Prog

(Python)
def A074939(n): return int(bin((n.bit_count()&1)+(n<<1))[2:], 3) # Chai Wah Wu, Jun 26 2025

Crossrefs

Intersection of A005843 and A005836.

Cf. A006996, A010060, A055246, A074938, A083095.

Sequence in context: A175436 A390944 A354024 * A038464 A366633 A360037

Adjacent sequences: A074936 A074937 A074938 * A074940 A074941 A074942

Keyword

easy,nonn

Author

Benoit Cloitre, Oct 04 2002; Nov 15 2003

Status

approved