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Search: id:A023057
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| A023057 |
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(Apparently) not the difference between adjacent perfect powers (A001597, integers of form a^b, a >= 1, b >= 2). |
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+0
8
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| 6, 14, 22, 29, 31, 34, 42, 44, 46, 50, 52, 54, 58, 62, 64, 66, 70, 72, 78, 82, 84, 86, 88, 90, 91, 96, 98, 102, 105, 110, 111, 114, 117, 118, 120, 122, 124, 126, 130, 132, 134, 136, 140, 142, 153, 156, 158, 160, 162, 164, 165, 172, 176, 177, 178, 179, 181, 182, 188, 190
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Catalan's conjecture (now a theorem) is that 1 occurs just once as a difference, between 8 and 9.
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REFERENCES
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G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
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LINKS
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Alf van der Poorten, Remarks on the sequence of 'perfect' powers
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MATHEMATICA
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pp = Union[ Join[{1}, Flatten[ Table[n^i, {n, 2, Sqrt[10^12]}, {i, 2, Log[n, 10^12]}]]]]; l = Length[pp]; d = Sort[Take[pp, -l + 1] - Take[pp, l - 1]]; Complement[ Table[i, {i, 1, 200}], Take[ Union[d], 200]] (from Robert G. Wilson v)
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CROSSREFS
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Cf. A001597 (perfect powers), A023055 (complement). See also A074980, A074981, A077286.
Sequence in context: A110223 A125086 A138290 this_sequence A062316 A079299 A043445
Adjacent sequences: A023054 A023055 A023056 this_sequence A023058 A023059 A023060
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KEYWORD
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nonn,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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