A335119 Number of positive terms of A082916 not exceeding 10^n.

5, 33, 233, 1734, 13487, 111460, 950039, 8282970, 73631430, 662319904, 6022446576, 55201746383

Offset: 1

Author

Amiram Eldar, May 24 2020

Keywords

• nonn
• more

Examples

			Below 10 there are 5 positive terms of A082916: 1, 3, 5, 7, 9. Therefore a(1) = 5.
		

Links

• Kevin Ford and Sergei Konyagin, Divisibility of the central binomial coefficient binomial(2n, n), arXiv:1909.03903 [math.NT], 2019. See Table 2.

Crossrefs

Cf. A000984, A082916.

Programs

Mathematica

seqQ[n_] := CoprimeQ[Binomial[2*n, n], n]; seq = {}; p = 10; c = 0; Do[If[seqQ[n], c++]; If[n == p, p *= 10; AppendTo[seq, c]], {n, 1, 10^5}]; seq

Formula

a(n) ~ c * 10^n/log(10^n), where c = 1.526453... (Ford and Konyagin, 2019).

Extensions

Terms a(4)-a(11) were taken from the paper by Ford and Konyagin (2019).

a(12) from Giovanni Resta, May 24 2020