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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.

%I A321132 #8 Nov 09 2018 20:53:08
%S A321132 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,
%T A321132 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,
%U A321132 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
%N 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.
%C A321132 All primes are either on the main line or will join it before reaching 0, as in A060197 or 1, as in A071578.
%C A321132 First occurrence of k, k=0,1,2,...: 1, 4, 7, 17, 59, 277, 1787, 15299, 167449, 2269733, etc.
%C A321132 A measure of Primeness - see the Fernandez link.
%H A321132 Neil Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>
%F A321132 a(n) = 0 iff n is a member of A007097.
%e A321132 a(10) is 3 because the tenth prime is 29 -> 10 -> 4 -> 2 and 2 is A007097(1).
%t A321132 f[n_] := Length@ NestWhileList[PrimePi, n, ! MemberQ[{1, 2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041}, #] &] - 1; Array[f, 105]
%Y A321132 Cf. A000720, A007097, A049076, A060197, A071578, A114537.
%K A321132 nonn
%O A321132 1,4
%A A321132 _Robert G. Wilson v_, Oct 27 2018