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a(n) is the number of terms of A000057 in [10^n].
0

%I #25 Jun 22 2024 04:48:13

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

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

%H Rishi Kumar, <a href="https://arxiv.org/abs/2406.05890">Kepler Sets of Second-Order Linear Recurrence Sequences Over Q_p</a>, arXiv:2406.05890 [math.NT], 2024. See pp. 6-7.

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

%t 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 *)

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

%K nonn,hard,more

%O 1,1

%A _Stefano Spezia_, Jun 18 2024