A092831 Indices of prime Motzkin numbers.

2, 7, 12, 36

Offset: 1

Author

Eric W. Weisstein, Mar 06 2004

Keywords

• nonn
• more

Comments

Next term > 10^5. - Joerg Arndt, Oct 17 2016

From Serge Batalov, Feb 02 2022: (Start)

Next term (if it exists) > 2*10^7.

This sequence may be finite, for the reason that with increasing n, the density of trivially composite Motzkin numbers approaches 1. For 7*10^6 < n < 20*10^6, all Motzkin numbers have a small factor not exceeding 63809. See below.

Rowland and Yassawi, and later Burns, established asymptotic densities of A001006(n) modulo primes up to 29. In particular, the asymptotic densities of A001006(n) == 0 modulo 3, 7, 17 or 19 are 1. (End)

Links

• Rob Burns, Structure and asymptotics for Motzkin numbers modulo small primes using automata, arXiv:1612.08146 [math.NT], 2016.
• E. Rowland and R. Yassawi, Automatic congruences for diagonals of rational functions, arXiv preprint arXiv:1310.8635 [math.NT], 2013-2014.
• Eric Weisstein's World of Mathematics, Motzkin Number
• Eric Weisstein's World of Mathematics, Integer Sequence Primes

Crossrefs

Cf. A001006, A092832.