A054575 Number of iterations to reach new prime in A054574.

4, 2, 2, 2, 3, 2, 2, 2, 2, 2, 5, 2, 10, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 4, 2, 3, 3, 3, 2, 3, 3, 2, 2, 6, 18, 2, 2, 2, 16, 3, 16, 4, 2, 2, 4, 3, 2, 4, 2, 2, 5, 3, 2, 3, 2, 3, 4, 6, 3, 2, 12, 10, 2, 2, 4, 2, 4, 2, 2, 10, 2, 4, 3, 2, 4, 2, 3, 2, 2, 9, 6, 2, 2, 20, 3, 2, 3, 3, 3, 2, 10, 15, 2, 2, 11, 10

Offset: 1

Author

Enoch Haga, Apr 11 2000

Keywords

• easy
• nonn

Examples

			a(5)=3 because beginning at 11, the next prime, 47, is attained in 3 steps.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054574.

Programs

Mathematica

f[n_] := n + Plus @@ Times @@@ FactorInteger@n; a[n_] := Length[NestWhileList[f, (p = Prime[n]), # == p || CompositeQ[#] &]] - 1; Array[a, 100] (* Amiram Eldar, Sep 07 2019 *)