A236536 Array T(n,k) read along antidiagonals: the composites of order of compositeness n in row n.

4, 6, 9, 8, 12, 16, 10, 15, 21, 26, 14, 18, 25, 33, 39, 20, 24, 28, 38, 49, 56, 22, 32, 36, 42, 55, 69, 78, 27, 34, 48, 52, 60, 77, 94, 106, 30, 40, 50, 68, 74, 84, 105, 125, 141, 35, 45, 57, 70, 93, 100, 115, 140, 164, 184, 44, 51, 64, 80, 95, 124, 133, 152, 183, 212, 236, 46, 63, 72, 88, 110, 126, 162, 174, 198, 235, 270, 299

Offset

1,1

Comments

Row n contains the composites A002808(j) for which A059981(j) = n.

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.

Links

Table of n, a(n) for n=1..78.

Formula

T(1,k) = A022449(k).

T(n,k) = A002808( T(n-1,k) ), n>1 .

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

A236536 := proc(n, k)
    option remember ;
    if n = 1 then
        A022449(k) ;
    else
        A002808(procname(n-1, k)) ;
    end if:
end proc:
for d from 2 to 10 do
     for k from d-1 to  by -1 do
        printf("%3d, ", A236536(d-k, k)) ;
     end do:
end do:

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

Cf. A006508 (column 1), A022449 (row 1), A135044, A236542, A002808.

Sequence in context: A073870 A236025 A218036 * A084335 A277893 A197575

Adjacent sequences: A236533 A236534 A236535 * A236537 A236538 A236539

Keyword

nonn,easy,tabl

Author

R. J. Mathar, Jan 28 2014

Status

approved