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A072491
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Define f(1) = 0. For n>=2, let f(n) = n - p where p is the largest prime <= n. a(n) = number of iterations of f to reach 0, starting from n.
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3
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1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 3, 2, 1, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 3, 2, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2
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OFFSET
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1,4
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COMMENTS
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a(p)=1, a(p+1)=2 and a(p+4)=3 if p is an odd prime but p+2 and p+4 are composite.
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REFERENCES
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S. S. Pillai, "An arithmetical function concerning primes", Annamalai University Journal (1930), pp. 159-167.
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LINKS
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Table of n, a(n) for n=1..105.
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FORMULA
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On Cramér's conjecture, a(n) = O(log* n). - Charles R Greathouse IV, Feb 04 2013
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EXAMPLE
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a(27)=3 as f(27)=27-23=4, f(4)=4-3=1 and f(1)=0.
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MATHEMATICA
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f[1]=0; f[n_] := n-Prime[PrimePi[n]]; a[n_] := Module[{k, x}, For[k=0; x=n, x>0, k++; x=f[x], Null]; k]
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PROG
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(PARI) a(n)=if(n<4, n>0, 1+a(n-precprime(n))) \\ Charles R Greathouse IV, Feb 04 2013
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CROSSREFS
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Cf. A072492. A066352(n) is the smallest k such that a(k)=n.
Not the same as A051034: a(122) = 3, but A051034(122) = 2.
Sequence in context: A071854 A183025 A072410 * A051034 A082477 A036430
Adjacent sequences: A072488 A072489 A072490 * A072492 A072493 A072494
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KEYWORD
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nonn,easy
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 14 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Nov 26 2002
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STATUS
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approved
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