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A280267 Square array read by rows: H_k(n,n), with rows n >= 0 and columns 0 <= k <= 3, where H_n is the n-th hyperoperation. 1
1, 0, 0, 1, 2, 2, 1, 1, 3, 4, 4, 4, 4, 6, 9, 27, 5, 8, 16, 256, 6, 10, 25, 3125, 7, 12, 36, 46656, 8, 14, 49, 823543, 9, 16, 64, 16777216, 10, 18, 81, 387420489, 11, 20, 100, 10000000000, 12, 22, 121, 285311670611, 13, 24, 144, 8916100448256, 14, 26, 169, 302875106592253 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
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,n) for some n.
LINKS
EXAMPLE
Square array begins:
1, 0, 0, 1;
2, 2, 1, 1;
3, 4, 4, 4;
4, 6, 9, 27;
5, 8, 16, 256;
6, 10, 25, 3125;
7, 12, 36, 46656;
8, 14, 49, 823543;
9, 16, 64, 16777216;
10, 18, 81, 387420489;
11, 20, 100, 10000000000;
12, 22, 121, 285311670611;
13, 24, 144, 8916100448256;
14, 26, 169, 302875106592253;
...
For line n=10 we have:
H_0(10,10) = 11.
H_1(10,10) = 20.
H_2(10,10) = 100.
H_3(10,10) = 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, n], {n, 0, 20}, {k, 0, 3}]
CROSSREFS
Cf. A054871, A280265 (table of H_k(n,2)).
Sequence in context: A292508 A237597 A034928 * A161671 A144444 A054106
KEYWORD
nonn,tabf
AUTHOR
Natan Arie Consigli, Dec 30 2016
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)