A082081 a(n) = fixed point when the pseudo-log function A008475[ ] is iterated.

0, 2, 3, 4, 5, 5, 7, 8, 9, 7, 11, 7, 13, 9, 8, 16, 17, 11, 19, 9, 7, 13, 23, 11, 25, 8, 27, 11, 29, 7, 31, 32, 9, 19, 7, 13, 37, 7, 16, 13, 41, 7, 43, 8, 9, 25, 47, 19, 49, 27, 9, 17, 53, 29, 16, 8, 13, 31, 59, 7, 61, 9, 16, 64, 11, 16, 67, 7, 8, 9, 71, 17, 73, 16, 11, 23, 11, 11, 79, 7, 81

Offset: 1

Author

Labos Elemer, Apr 08 2003

Keywords

• nonn

Comments

Fixed point is always a prime or a power of prime: fixed points are terms of A000961.

Examples

			n=10!=3628800:list to fixed point={3628800,369,50,27}.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008475, A001414, A056239, A029908, A082083.

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]}] sex[x_] := Apply[Plus, ba[x]^ep[x]] Table[FixedPoint[sex, w], {w, 1, 128}]