A280265 - OEIS

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

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OFFSET

0,1

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.

LINKS

Table of n, a(n) for n=0..64.

EXAMPLE

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;

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}]

CROSSREFS

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

Sequence in context: A117406 A290216 A293202 * A292795 A295028 A294201

Adjacent sequences: A280262 A280263 A280264 * A280266 A280267 A280268

KEYWORD

nonn,tabf,easy

AUTHOR

Natan Arie Consigli, Dec 30 2016

EXTENSIONS

Definition corrected by Natan Arie Consigli, Jun 13 2017

STATUS

approved