A354967 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).

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, 127, 8, 17, 41, 127, 277, 709, 709, 709, 9, 19, 59, 179, 709, 1787, 5381, 5381, 5381, 10, 23, 67, 277, 1063, 5381, 15299, 52711, 52711, 52711, 11, 29, 83, 331, 1787, 8527, 52711, 167449, 648391, 648391, 648391

Offset: 1

Author

Rémy Sigrist, Jun 14 2022

Keywords

• nonn
• tabl
• easy

Comments

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

Examples

			Array A(n, k) begins:
  n\k|  0   1   2    3     4      5       6        7         8
  ---+--------------------------------------------------------
    1|  1   2   3    5    11     31     127      709      5381
    2|  2   3   5   11    31    127     709     5381     52711
    3|  3   5  11   31   127    709    5381    52711    648391
    4|  4   7  17   59   277   1787   15299   167449   2269733
    5|  5  11  31  127   709   5381   52711   648391   9737333
    6|  6  13  41  179  1063   8527   87803  1128889  17624813
    7|  7  17  59  277  1787  15299  167449  2269733  37139213
    8|  8  19  67  331  2221  19577  219613  3042161  50728129
		

Crossrefs

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

Programs

PARI

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

Formula

A(n, 0) = n.

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

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

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

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

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

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

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

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

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

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

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