login
A236536
Array T(n,k) read along antidiagonals: the composites of order of compositeness n in row n.
5
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.
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: A236025 A377181 A218036 * A084335 A277893 A197575
KEYWORD
nonn,easy,tabl
AUTHOR
R. J. Mathar, Jan 28 2014
STATUS
approved