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

1,4

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.

Links

Table of n, a(n) for n=1..105.

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

Formula

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

Example

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

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]

Crossrefs

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

Sequence in context: A323212 A185815 A332448 * A003987 A307302 A307297

Adjacent sequences: A321129 A321130 A321131 * A321133 A321134 A321135

Keyword

nonn

Author

Robert G. Wilson v, Oct 27 2018

Status

approved