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A370775
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Integers m whose (constant) convergence speed is exactly 2 (i.e., m^^(m+1) has 2 more rightmost frozen digits than m^^m, where ^^ indicates tetration).
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1
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5, 7, 18, 24, 26, 32, 35, 43, 45, 49, 51, 74, 75, 76, 82, 85, 93, 99, 107, 115, 118, 125, 132, 143, 149, 151, 155, 157, 165, 168, 174, 176, 195, 199, 201, 205, 207, 218, 224, 226, 232, 235, 243, 245, 251, 257, 268, 274, 275, 276, 282, 285, 293, 299, 301, 307
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OFFSET
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1,1
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COMMENTS
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It is well known (see Links) that as the hyperexponent of the integer m becomes sufficiently large, the constant convergence speed of m is the number of new stable digits that appear at the end of the result for any further unit increment of the hyperexponent itself, and a sufficient (but not necessary) condition to get this fixed value is to set the hyperexponent equal to m plus 1.
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LINKS
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FORMULA
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a(n) is such that A317905(m) = 2, for m = 5, 6, 7, ...
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EXAMPLE
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If n = 2, m = 7 and so 7^^8 has exactly 2 more stable digits at the end of the result than 7^^7.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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