A280265 Array with five columns read by rows: H_k(n,2), with rows n >= 0 and columns 0 <= k <= 4, where H_n is the n-th hyperoperation.

3, 2, 0, 1, 1, 3, 3, 2, 1, 1, 3, 4, 4, 4, 4, 3, 5, 6, 9, 27, 3, 6, 8, 16, 256, 3, 7, 10, 25, 3125, 3, 8, 12, 36, 46656, 3, 9, 14, 49, 823543, 3, 10, 16, 64, 16777216, 3, 11, 18, 81, 387420489, 3, 12, 20, 100, 10000000000, 3, 13, 22, 121, 285311670611, 3, 14, 24, 144, 8916100448256

Offset: 0

Author

Natan Arie Consigli, Dec 30 2016

Keywords

• nonn
• tabf
• easy

Comments

See A054871 for definitions and key links.

The purpose of this sequence is to unify all the visible terms of the sequence: a(k)= H_k(n,2) for some n.

Examples

			Square array begins:
3, 2,  0,  1,   1;
3, 3,  2,  1,   1;
3, 4,  4,  4,   4;
3, 5,  6,  9,   27;
3, 6,  8,  16,  256;
3, 7,  10, 25,  3125;
3, 8,  12, 36,  46656;
3, 9,  14, 49,  823543;
3, 10, 16, 64,  16777216;
3, 11, 18, 81,  387420489;
3, 12, 20, 100, 10000000000;
3, 13, 22, 121, 285311670611;
3, 14, 24, 144, 8916100448256;
...
For row 10 we have:
H_0(10,2) = 3;
H_1(10,2) = 12;
H_2(10,2) = 20;
H_3(10,2) = 100;
H_4(10,2) = 10000000000;
		

Crossrefs

Cf. A054871, A256131 (contains only line n=10), A280267, A000312.

Programs

Mathematica

H[0, x_, y_] := y + 1;
H[1, x_, y_] := x + y;
H[2, x_, y_] := x*y;
H[3, x_, y_] := x^y;
H[4, x_, 2] := x^x;
Table[H[k, n, 2], {n, 0, 20}, {k, 0, 4}]

Extensions

Definition corrected by Natan Arie Consigli, Jun 13 2017