A089118 Nonnegative numbers in (3*A005836 - 1) [A005836 are the numbers with base representation containing no 2].

2, 8, 11, 26, 29, 35, 38, 80, 83, 89, 92, 107, 110, 116, 119, 242, 245, 251, 254, 269, 272, 278, 281, 323, 326, 332, 335, 350, 353, 359, 362, 728, 731, 737, 740, 755, 758, 764, 767, 809, 812, 818, 821, 836, 839, 845, 848, 971, 974, 980, 983, 998, 1001, 1007, 1010

Offset: 1

Author

Emeric Deutsch and Bruce E. Sagan, Dec 05 2003

Keywords

• nonn
• base

Comments

Numbers k such that the Motzkin number A001006(k) == 2 (mod 3).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Rob Burns, Asymptotic density of Motzkin numbers modulo small primes, arXiv:1611.04910 [math.NT], 2016.

Crossrefs

Cf. A005836, A001006, A082575, A089119.

Programs

Mathematica

(* m = MotzkinNumber *) m[0] = 1; m[n_] := m[n] = m[n - 1] + Sum[ m[k]*m[n - 2 - k], {k, 0, n - 2}]; Select[ Range[1010], Mod[m[#], 3] == 2 &] (* Jean-François Alcover, Jul 10 2013 *)
Select[3*Range[350] - 1, DigitCount[# + 1, 3, 2] == 0 &] (* Amiram Eldar, Jun 04 2022 *)

Extensions

Offset corrected to 1 by Jean-François Alcover, Jun 23 2016