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A049076
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Number of steps in the prime index chain for the n-th prime.
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39
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1, 2, 3, 1, 4, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1
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OFFSET
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1,2
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COMMENTS
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Let p(k) = k-th prime, let S(p) = S(p(k)) = k, the subscript of p; a(n) = order of primeness of p(n) = 1+m where m is largest number such that S(S(..S(p(n))...)) with m S's is a prime.
The record holders correspond to A007097.
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LINKS
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N. Fernandez, Table of n, a(n) for n = 1..500
N. Fernandez, An order of primeness, F(p)
N. Fernandez, The Exploring Primeness Project
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FORMULA
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Let b(n) = 0 if n is nonprime, otherwise b(n) = k where n is the k-th prime. Then a(n) is the number of times you can apply b to the n-th prime before you hit a nonprime.
a(n) = 1 +A078442(n). - R. J. Mathar, Jul 07 2012
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EXAMPLE
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11 is 5th prime, so S(11)=5, 5 is 3rd prime, so S(S(11))=3, 3 is 2nd prime, so S(S(S(11)))=2, 2 is first prime, so S(S(S(S(11))))=1, not a prime. Thus a(5)=4.
Alternatively, a(5) = 4: the 5th prime is 11 and its prime index chain is 11->5->3->2->1->0. a(6) = 1: the 6th prime is 13 and its prime index chain is 13->6->0.
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MATHEMATICA
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A049076[n_] := Length[ NestWhileList[ PrimePi, n, PrimeQ]]; Table[ f[n], {n, 105}] (from Robert G. Wilson v, Mar 11 2004)
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PROG
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(PARI) apply(p->my(s=1); while(isprime(p=primepi(p)), s++); s, primes(100)) \\ Charles R Greathouse IV, Nov 20 2012
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CROSSREFS
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Cf. A049077, A049078, A049079, A049080, A049081, A006450.
Sequence in context: A039661 A214684 A081877 * A097744 A055445 A135560
Adjacent sequences: A049073 A049074 A049075 * A049077 A049078 A049079
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KEYWORD
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nice,nonn,easy
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AUTHOR
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Neil Fernandez
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EXTENSIONS
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Additional comments from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 12 2003
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STATUS
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approved
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