A321132 a(n) is the number of iterations of the mapping of x -> pi(x) until n reaches the main line as defined by A007097.

0, 0, 0, 2, 0, 2, 3, 3, 3, 3, 0, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

Robert G. Wilson v, Oct 27 2018

Keywords

• nonn

Comments

All primes are either on the main line or will join it before reaching 0, as in A060197 or 1, as in A071578.

First occurrence of k, k=0,1,2,...: 1, 4, 7, 17, 59, 277, 1787, 15299, 167449, 2269733, etc.

A measure of Primeness - see the Fernandez link.

Examples

			a(10) is 3 because the tenth prime is 29 -> 10 -> 4 -> 2 and 2 is A007097(1).
		

Links

• Neil Fernandez, An order of primeness, F(p)

Crossrefs

Cf. A000720, A007097, A049076, A060197, A071578, A114537.

Programs

Mathematica

f[n_] := Length@ NestWhileList[PrimePi, n, ! MemberQ[{1, 2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041}, #] &] - 1; Array[f, 105]

Formula

a(n) = 0 iff n is a member of A007097.