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

%I A236542 #14 Apr 18 2020 19:14:00
%S A236542 2,7,3,13,17,5,19,41,59,11,23,67,179,277,31,29,83,331,1063,1787,127,
%T A236542 37,109,431,2221,8527,15299,709,43,157,599,3001,19577,87803,167449,
%U A236542 5381,47,191,919,4397,27457,219613,1128889,2269733,52711
%N A236542 Array T(n,k) read along descending antidiagonals: row n contains the primes with n steps in the prime index chain.
%C A236542 Row n contains the primes A000040(j) for which A049076(j) = n.
%H A236542 N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>.
%F A236542 T(1,k) = A007821(k).
%F A236542 T(n,k) = prime( T(n-1,k) ), n>1 .
%e A236542 The array starts:
%e A236542     2,    7,   13,   19,   23,   29,   37,   43,   47,   53,...
%e A236542     3,   17,   41,   67,   83,  109,  157,  191,  211,  241,...
%e A236542     5,   59,  179,  331,  431,  599,  919, 1153, 1297, 1523,...
%e A236542    11,  277, 1063, 2221, 3001, 4397, 7193, 9319,10631,12763,...
%e A236542    31, 1787, 8527,19577,27457,42043,72727,96797,112129,137077,...
%p A236542 A236542 := proc(n,k)
%p A236542     option remember ;
%p A236542     if n = 1 then
%p A236542         A007821(k) ;
%p A236542     else
%p A236542         ithprime(procname(n-1,k)) ;
%p A236542     end if:
%p A236542 end proc:
%p A236542 for d from 2 to 10 do
%p A236542     for k from d-1 to 1 by -1 do
%p A236542             printf("%d,",A236542(d-k,k)) ;
%p A236542     end do:
%p A236542 end do:
%t A236542 A007821 = Prime[Select[Range[15], !PrimeQ[#]&]];
%t A236542 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]]];
%t A236542 Table[T[n-k+1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Apr 16 2020 *)
%Y A236542 Cf. A007821 (row 1), A049078 (row 2), A049079 (row 3), A007097 (column 1), A058010 (diagonal), A057456 - A057457 (columns), A135044, A236536.
%K A236542 nonn,tabl
%O A236542 1,1
%A A236542 _R. J. Mathar_, Jan 28 2014