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A064722
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a(1) = 0; for n >= 2, a(n) = n - (largest prime <= n).
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7
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0, 0, 0, 1, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3
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OFFSET
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1,9
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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a(n) = 0 iff n is 1 or a prime.
Computable also as a "commutator": PrimePi[Prime[m]]-Prime[PrimePi[m]]= A000720[A000040(m)]-A000040[A000720(m)]. Labels position of composites between 2 consecutive primes. - Labos E. (labos(AT)ana.sot.hu), Oct 19 2001
a(n) = a(n-1)*0^A010051(n) + 1 - A010051(n), a(1) = 0. - Reinhard Zumkeller, Mar 23 2006
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EXAMPLE
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a(26) = 26 - 23 = 3, a(37) = 37 - 37 = 0.
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MATHEMATICA
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Join[{0}, Table[n-NextPrime[n+1, -1], {n, 2, 110}]] (* From Harvey P. Dale, Aug 23 2011 *)
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PROG
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(PARI) { for (n = 1, 1000, if (n>1, a=n - precprime(n), a=0); write("b064722.txt", n, " ", a) ) } [From Harry J. Smith, Sep 23 2009]
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CROSSREFS
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Equals n - A007917(n).
Cf. A007920
Sequence in context: A123343 A054439 A215151 * A123735 A155839 A135814
Adjacent sequences: A064719 A064720 A064721 * A064723 A064724 A064725
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Oct 13 2001
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STATUS
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approved
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