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A098879
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a(n) = (2^n - 1)^5 - 2.
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1
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-2, -1, 241, 16805, 759373, 28629149, 992436541, 33038369405, 1078203909373, 34842114263549, 1120413075641341, 35940921946155005, 1151514816750309373, 36870975646169341949, 1180231376725002502141, 37773167607267111108605, 1208833588708967444709373
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OFFSET
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0,1
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COMMENTS
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5th-power analog of what for exponent 2 is A093112 (2^n-1)^2 - 2 = 4^n - 2^{n+1} - 1 and exponent 3 is A098878 (2^n - 1)^3 - 2. Primes include a(n) for n = 0, 2, 5, 6. These are "near-5th-power prime." Semiprimes include a(n) for n = 3, 8, 9, 10, 13, 15, 21, 29, 33, 40. - Jonathan Vos Post, May 03 2006
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LINKS
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FORMULA
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G.f.: (-2+125*x-2300*x^2+22640*x^3-57728*x^4+66560*x^5)/((-1+x)(-1+32*x)(-1+16*x)(-1+8*x)(-1+4*x)(-1+2*x)). - R. J. Mathar, Nov 14 2007
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EXAMPLE
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If n=2, (2^2 - 1)^5 - 2 = 241 (a prime).
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MATHEMATICA
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(2^Range[0, 20]-1)^5-2 (* or *) LinearRecurrence[{63, -1302, 11160, -41664, 64512, -32768}, {-2, -1, 241, 16805, 759373, 28629149}, 20] (* Harvey P. Dale, Nov 03 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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