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A280265
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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.
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1
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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
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0,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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;
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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