A059981 Order of compositeness for the n-th composite number.

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

Offset

1,4

Comments

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 composite.

Number of steps in the composite index chain for the n-th composite. - Daniel Forgues, Sep 28 2012

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Example

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.
4 is the first composite number, so S(4)=1, not a composite number. Thus a(1)=1.

Mathematica

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; Table[ c = 1; k = CompositePi[ Composite[ n ] ]; While[ ! (PrimeQ[ k ] || k == 1), k = CompositePi[ k ]; c++ ]; c, {n, 100} ]

Crossrefs

Cf. A049076, A022449 (composites with compositeness 1).

Sequence in context: A366521 A348581 A124044 * A033676 A095165 A355366

Adjacent sequences: A059978 A059979 A059980 * A059982 A059983 A059984

Keyword

easy,nonn

Author

Robert G. Wilson v, Mar 06 2001

Status

approved