A373774 a(n) is the number of terms of A000057 in [10^n].

3, 7, 38, 249, 1894, 15456, 130824, 11344404, 10007875, 89562047

Offset: 1

Author

Stefano Spezia, Jun 18 2024

Keywords

• nonn
• hard
• more

Links

• Rishi Kumar, Kepler Sets of Second-Order Linear Recurrence Sequences Over Q_p, arXiv:2406.05890 [math.NT], 2024. See pp. 6-7.

Crossrefs

Cf. A000045, A000057, A001602, A005596, A006880.

Programs

Mathematica

a[n_]:=Length[Select[Prime[Range[PrimePi[10^n]]], Function[p, c=0; b=1; m=1; While[b != 0, t=b; b = Mod[(c+b), p]; c=t; m++]; m>p]]]; Array[a,4] (* after Charles R Greathouse IV and Jean-François Alcover in A000057 *)

Formula

Conjectured by Kumar under GRH: Limit_{n->oo} a(n)/A006880(n) = (10/19)*A005596 = 0.196818849273264362134067397024429692164015394...