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

Author

Benoit Cloitre, Oct 04 2002; Nov 15 2003

Keywords

• easy
• nonn

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.

Crossrefs

Intersection of A005843 and A005836.

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

Programs

Mathematica

Select[2*Range[0,600],DigitCount[#,3,2]==0&] (* Harvey P. Dale, Dec 10 2016 *)

Python

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

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