cp's OEIS Frontend

A380334 Decimal expansion of the smallest possible average gap for the prime number subsequence P" = A262275.

%I A380334 #32 Jan 29 2025 16:35:06
%S A380334 9,4,5,1,9,3,9,8,1,3,4,4,7,8,0,6,3,1,1,4,1,0,7,5,0,2,2,4,7,0,8,4,0,4,
%T A380334 2,1,7,5,4,2,0,4,5,1,5,5,4,8,6,7,9,6,2,6,3,0,9,1,6,8,3,2,3,6,5,0,5,4,
%U A380334 8,7,9,5,6,5,9,6,7,6,5,2,1,0,6,1,0,0,9,7,8,7,0,9,0,8,4,1,9,6,6
%N A380334 Decimal expansion of the smallest possible average gap for the prime number subsequence P" = A262275.
%F A380334 Equals x*(x-1) where x = A338460.
%e A380334 9.45193981344780631141075022470840...
%t A380334 f[x_] := Log[x!]*{Log[x!]+1}-x*{x-1};
%t A380334 root = FindRoot[f[x]  == 0, {x, 3},WorkingPrecision -> 100];
%t A380334 y=root;
%t A380334 z=x/. y;
%t A380334 RealDigits[Log[z!]*{Log[z!]+1}]
%o A380334 (PARI) my(y=solve(x=3, 4, lngamma(x+1)-x+1)); y*(y-1) \\ _Michel Marcus_, Jan 28 2025
%Y A380334 Cf. A262275, A338460.
%K A380334 nonn,cons
%O A380334 1,1
%A A380334 _Michael P. May_, Jan 21 2025