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Search: id:A059981
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| A059981 |
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Order of compositeness of n. |
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+0
3
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| 1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 4, 1, 3, 1, 2, 4, 2, 1, 3, 4, 5, 2, 4, 1, 2, 1, 3, 5, 3, 2, 4, 1, 5, 6, 3, 1, 5, 1, 2, 3, 2, 1, 4, 6, 4, 3, 5, 1, 2, 6, 7, 4, 2, 1, 6, 1, 2, 3, 4, 3, 2, 1, 5, 7, 5, 1, 4, 1, 6, 2, 3, 7, 8, 1, 5, 3, 2, 1, 7, 2, 3, 4, 5, 1, 4, 3, 2, 6, 8, 6, 2, 1, 5, 2, 7
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Let c(k) = k-th composite number, let S(c) = S(c(k)) = k, the subscript of c; a(n) = order of compositeness of c(n) = 1+m where m is largest number such that S(S(..S(c(n))...)) with m S's is a not prime.
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EXAMPLE
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16 is 9th composite number, so S(16)=9, 9 is 4th composite, so S(S(16))=4, 4 is first composite number, so S(S(S(16)))=1, not a composite number. Thus a(9)=3.
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MATHEMATICA
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Composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k != n + PrimePi[ k ] + 1, k++ ]; k); CompositePi[ n_Integer ] := (n - 1 - PrimePi[ n ]); Attributes[ Composite ] = Attributes[ CompositePi ] = Listable; Do[ c = 1; k = CompositePi[ Composite[ n ] ]; While[ ! (PrimeQ[ k ] || k == 1), k = CompositePi[ k ]; c++ ]; Print[ c ], {n, 1, 100} ]
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CROSSREFS
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Cf. A049076.
Sequence in context: A137866 A072203 A124044 this_sequence A033676 A095165 A046805
Adjacent sequences: A059978 A059979 A059980 this_sequence A059982 A059983 A059984
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KEYWORD
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easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 06 2001
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