A082084 a(n)=A029908[n! ]=A029908[A000142[n]] Fixed points of iterated A001414 function if started at factorials as initial values.

0, 2, 5, 5, 5, 19, 5, 7, 7, 11, 13, 13, 23, 13, 19, 101, 61, 5, 19, 5, 11, 5, 5, 7, 23, 7, 5, 7, 283, 293, 5, 5, 7, 367, 379, 389, 23, 7, 463, 5, 13, 11, 29, 5, 23, 7, 7, 19, 5, 5, 5, 5, 61, 7, 73, 47, 857, 7, 947, 5, 29, 7, 13, 5, 5, 19, 137, 7, 5, 7, 11, 23, 353, 53, 11, 1471, 1489

Offset: 1

Author

Labos Elemer, Apr 08 2003

Keywords

• nonn

Examples

			Fixed point seems to be always a prime:tested for 1<n<201
n=20!=2432902008176640000: a(20)=5 with fixed-point-list=
{2432902008176640000,154,20,9,6,5,5}
		

Crossrefs

Cf. A001414, A056239, A008475, A082081-A082083, A000961, A000142.

Programs

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] slog[x_] := Apply[Plus, ba[x]*ep[x]] Table[FixedPoint[slog, w! ], {w, 1, 128}]