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

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..99.

Formula

Equals x*(x-1) where x = A338460.

Example

9.45193981344780631141075022470840...

Mathematica

f[x_] := Log[x!]*{Log[x!]+1}-x*{x-1};
root = FindRoot[f[x]  == 0, {x, 3}, WorkingPrecision -> 100];
y=root;
z=x/. y;
RealDigits[Log[z!]*{Log[z!]+1}]

Prog

(PARI) my(y=solve(x=3, 4, lngamma(x+1)-x+1)); y*(y-1) \\ Michel Marcus, Jan 28 2025

Crossrefs

Cf. A262275, A338460.

Sequence in context: A199179 A344949 A300072 * A062546 A245887 A336603

Adjacent sequences: A380331 A380332 A380333 * A380335 A380336 A380337

Keyword

nonn,cons

Author

Michael P. May, Jan 21 2025

Status

approved