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Search: id:A057897
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| A057897 |
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Numbers which can be written as m^k-k [with m and k > 1]. |
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+0
6
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| 2, 5, 7, 12, 14, 23, 24, 27, 34, 47, 58, 61, 62, 77, 79, 98, 119, 121, 122, 142, 167, 194, 213, 223, 238, 248, 252, 254, 287, 322, 340, 359, 398, 439, 482, 503, 509, 527, 574, 621, 623, 674, 723, 726, 727, 782, 839, 898, 959, 997, 1014, 1019, 1022, 1087, 1154
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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It may be that positive integers can be written as m^k-k (with m and k > 1) in at most one way [checked up to 10000]
All numbers < 10^16 of this form have a unique representation. The uniqueness question leads to a Pillai-like exponential Diophantine equation a^x-b^y = x-y for x > y > 1 and b > a > 1, which appears to have no solutions. - T. D. Noe (noe(AT)sspectra.com), Oct 06 2004
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MATHEMATICA
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nLim=1000; lst={}; Do[k=2; While[n=m^k-k; n<=nLim, AppendTo[lst, n]; k++ ], {m, 2, Sqrt[nLim]}]; Union[lst] (T. D. Noe)
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CROSSREFS
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Cf. A000325, A008865, A024024, A024037, A024050, A057895, A057898, A057899.
Cf. A099225 (numbers of the form m^k+k, with m and k > 1), A074981 (n such that there is no solution to Pillai's equation), A099226 (numbers that can be represented as both a^x+x and b^y-y, for some a, b, x, y > 1).
Sequence in context: A159699 A063217 A088821 this_sequence A022758 A129232 A088822
Adjacent sequences: A057894 A057895 A057896 this_sequence A057898 A057899 A057900
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Sep 26 2000
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