A236542 - OEIS

%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