A354967 - OEIS

%I #9 Feb 03 2023 20:48:46

%S 1,2,2,3,3,3,4,5,5,5,5,7,11,11,11,6,11,17,31,31,31,7,13,31,59,127,127,

%T 127,8,17,41,127,277,709,709,709,9,19,59,179,709,1787,5381,5381,5381,

%U 10,23,67,277,1063,5381,15299,52711,52711,52711,11,29,83,331,1787,8527,52711,167449,648391,648391,648391

%N Square array A(n, k), n > 0, k >= 0, read by antidiagonals upwards; A(n, k) is the image of n after k iterates of the prime function (A000040).

%C For any m > 0, m appears A049076(m) times in the array.

%F A(n, 0) = n.

%F A(n, k+1) = A000040(A(n, k)).

%F A(n, n) = A058009(n).

%F A(n, A000040(n)) = A344946(n).

%F A(n, 1) = A000040(n).

%F A(n, 2) = A006450(n).

%F A(n, 3) = A038580(n).

%F A(1, k) = A007097(k).

%F A(4, k) = A057450(k+1).

%F A(6, k) = A057451(k+1).

%F A(8, k) = A057452(k+1).

%F A(9, k) = A057453(k+1).

%e Array A(n, k) begins:

%e   n\k|  0   1   2    3     4      5       6        7         8

%e   ---+--------------------------------------------------------

%e     1|  1   2   3    5    11     31     127      709      5381

%e     2|  2   3   5   11    31    127     709     5381     52711

%e     3|  3   5  11   31   127    709    5381    52711    648391

%e     4|  4   7  17   59   277   1787   15299   167449   2269733

%e     5|  5  11  31  127   709   5381   52711   648391   9737333

%e     6|  6  13  41  179  1063   8527   87803  1128889  17624813

%e     7|  7  17  59  277  1787  15299  167449  2269733  37139213

%e     8|  8  19  67  331  2221  19577  219613  3042161  50728129

%o (PARI) A(n,k) = { my (v=n); for (i=1, k, v=prime(v)); return (v) }

%Y Cf. A000040, A006450, A007097, A038580, A049076, A057450, A057451, A057452, A057453, A058009, A114537, A344946.

%K nonn,tabl,easy

%O 1,2

%A _Rémy Sigrist_, Jun 14 2022