A236542 Array T(n,k) read along descending antidiagonals: row n contains the primes with n steps in the prime index chain.

2, 7, 3, 13, 17, 5, 19, 41, 59, 11, 23, 67, 179, 277, 31, 29, 83, 331, 1063, 1787, 127, 37, 109, 431, 2221, 8527, 15299, 709, 43, 157, 599, 3001, 19577, 87803, 167449, 5381, 47, 191, 919, 4397, 27457, 219613, 1128889, 2269733, 52711

Offset

1,1

Comments

Row n contains the primes A000040(j) for which A049076(j) = n.

Links

Table of n, a(n) for n=1..45.

N. Fernandez, An order of primeness, F(p).

Formula

T(1,k) = A007821(k).

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

Example

The array starts:
    2,    7,   13,   19,   23,   29,   37,   43,   47,   53,...
    3,   17,   41,   67,   83,  109,  157,  191,  211,  241,...
    5,   59,  179,  331,  431,  599,  919, 1153, 1297, 1523,...
   11,  277, 1063, 2221, 3001, 4397, 7193, 9319,10631,12763,...
   31, 1787, 8527,19577,27457,42043,72727,96797,112129,137077,...

Maple

A236542 := proc(n, k)
    option remember ;
    if n = 1 then
        A007821(k) ;
    else
        ithprime(procname(n-1, k)) ;
    end if:
end proc:
for d from 2 to 10 do
    for k from d-1 to 1 by -1 do
            printf("%d, ", A236542(d-k, k)) ;
    end do:
end do:

Mathematica

A007821 = Prime[Select[Range[15], !PrimeQ[#]&]];
T[n_, k_] := T[n, k] = If[n == 1, If[k <= Length[A007821], A007821[[k]], Print["A007821 must be extended"]; Abort[]], Prime[T[n-1, k]]];
Table[T[n-k+1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Apr 16 2020 *)

Crossrefs

Cf. A007821 (row 1), A049078 (row 2), A049079 (row 3), A007097 (column 1), A058010 (diagonal), A057456 - A057457 (columns), A135044, A236536.

Sequence in context: A056756 A120861 A354368 * A279357 A099130 A362359

Adjacent sequences: A236539 A236540 A236541 * A236543 A236544 A236545

Keyword

nonn,tabl

Author

R. J. Mathar, Jan 28 2014

Status

approved