OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 1/10. It is a disjoint union of 4 sequences: numbers of the form (5*i + 1)*5^(2*j) - 2, (5*i + 2)*5^(2*j-1) - 1, (5*i + 3)*5^(2*j-1) - 2, and (5*i + 4)*5^(2*j) - 1, with i>=0 and j>=1, whose asymptotic densities are 1/120, 1/24, 1/24, and 1/120, respectively (Burns, 2016).
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.
EXAMPLE
9 is a term since A001006(9) = 835 = 5 * 167 is divisible by 5.
MATHEMATICA
motz[0] = motz[1] = 1; motz[n_] := motz[n] = ((2*n + 1)*motz[n - 1] + 3*(n - 1)*motz[n - 2])/(n + 2); Select[Range[0, 500], Divisible[motz[#], 5] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 30 2021
STATUS
approved