

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, 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
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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



