A292473 - OEIS

%I #12 Oct 28 2017 09:58:27

%S 2,3,11,5,23,29,7,37,43,157,13,41,47,173,113,17,59,53,181,151,223,19,

%T 67,71,229,163,239

%N Square array read by antidiagonals downwards: A(n,k) = k-th prime p such that A001222(2^p-1) = n.

%C A permutation of the prime numbers.

%C Is this the same as k-th prime p such that A001221(2^p-1) = n?

%e Array starts

%e     2,   3,   5,   7,  13,  17, ....

%e    11,  23,  37,  41,  59,  67, ....

%e    29,  43,  47,  53,  71,  73, ....

%e   157, 173, 181, 229, 233, 263, ....

%e   113, 151, 163, 191, 251, 307, ....

%e   223, 239, 359, 463, 587, 641, ....

%e   ....

%e A(2, 3) = 37, because the 3rd prime p such that 2^p-1 has 2 prime factors is 37, with 2^37-1 = 223 * 616318177.

%t With[{s = Array[PrimeOmega[2^Prime@ # - 1] &, 50]}, Function[t, Function[u, Table[Prime@ u[[#, k]] &[n - k + 1], {n, Length@t}, {k, n, 1, -1}]]@ Map[PadRight[#, Length@ t] &, t]]@ Values@ KeySort@ PositionIndex@ s] // Flatten (* _Michael De Vlieger_, Sep 17 2017 *)

%Y Cf. A000043 (row 1), A135978 (row 2), A140745 (column 1).

%Y Cf. A001222, A088863.

%K nonn,tabl,hard,more

%O 1,1

%A _Felix Fröhlich_, Sep 17 2017

%E More terms from _Michael De Vlieger_, Sep 17 2017