OFFSET
1,1
COMMENTS
The 1st row contains the composites with a nonprime index, A002808(1)=4, A002808(2)=6, A002808(3)=8, A002808(5)=10, A002808(7)=14,...
The 2nd row contains the composites with an index in the 1st row.
Recursively the followup rows contain the composites that need a higher number of applications of A002808 to reach a nonprime.
EXAMPLE
The array starts:
4, 6, 8, 10, 14, 20, 22, 27, 30, 35,...
9, 12, 15, 18, 24, 32, 34, 40, 45, 51,...
16, 21, 25, 28, 36, 48, 50, 57, 64, 72,...
26, 33, 38, 42, 52, 68, 70, 80, 88, 98,...
39, 49, 55, 60, 74, 93, 95,110,119,130,...
56, 69, 77, 84,100,124,126,145,156,170,...
78, 94,105,115,133,162,165,188,203,218,...
106,125,140,152,174,209,213,242,259,278,...
141,164,183,198,222,266,272,305,326,348,...
MAPLE
MATHEMATICA
Composite[n_] := FixedPoint[n + PrimePi[#] + 1&, n + PrimePi[n] + 1];
T[n_, k_] := T[n, k] = If[n == 1, Composite[If[k == 1, 1, Prime[k - 1]]], Composite[T[n - 1, k]]];
Table[T[n - k + 1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Sep 16 2023 *)
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Jan 28 2014
STATUS
approved