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