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

Author

R. J. Mathar, Jan 28 2014

Keywords

• nonn
• tabl

Comments

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

Examples

			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,...
		

Links

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

Crossrefs

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

Programs

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 *)

Formula

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

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