A073259 Number of iterations of f(n,k) = n+pi(k)+1 starting from f(n,n) until a fixed point is reached.

4, 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 4, 3, 4, 4, 3, 3, 3, 4, 4, 4, 3, 3, 3, 4, 4, 3, 4, 5, 4, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 4, 5, 4, 4, 3, 3, 4, 4, 4, 4, 5, 4, 4, 4, 3, 4, 4, 4, 5, 4, 4, 4, 3, 4, 4, 4, 4, 3, 3, 3, 4, 4, 4, 4, 5, 4, 4, 5, 5, 4, 4, 5, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 4, 4, 4, 3, 4, 5

Offset: 1

Author

Labos Elemer, Jul 22 2002

Keywords

• nonn

Comments

Original name: Length of FixedPointList leading to value of n-th composite number.

Examples

			n=1000000:the list={1000000,1078499,1084157,1084577,1084604,1084605}, its length including initial term is 6, while composite[1000000]=1084605.
		

Crossrefs

Cf. A000720, A064814, A002808, A073255-A073264.

Programs

Mathematica

Table[Length[FixedPointList[w+PrimePi[ # ]+1&, w]]-1, {w, 1, 128}]

Formula

See program below.

Extensions

Name clarified by Sean A. Irvine, Nov 21 2024