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Number of iterations of f(n,k) = n+pi(k)+1 starting from f(n,n) until a fixed point is reached.
5

%I #7 Nov 21 2024 20:18:33

%S 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,

%T 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,

%U 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

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

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

%F See program below.

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

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

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

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 22 2002

%E Name clarified by _Sean A. Irvine_, Nov 21 2024