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A155877
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Sums of three Fermat numbers.
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4
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9, 11, 13, 15, 23, 25, 27, 37, 39, 51, 263, 265, 267, 277, 279, 291, 517, 519, 531, 771, 65543, 65545, 65547, 65557, 65559, 65571, 65797, 65799, 65811, 66051, 131077, 131079, 131091, 131331, 196611, 4294967303, 4294967305, 4294967307
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OFFSET
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1,1
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COMMENTS
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Weisstein summarizes: "Ribenboim (1996, pp. 89 and 359-360) defines a generalized Fermat number as a number of the form a^(2^n)+1 with a>2, while Riesel (1994) further generalizes, defining it to be a number of the form a^(2^n) + b^(2^n). Both definitions generalize the usual Fermat numbers F_n = 2^(2^n)+1." In that context, the current sequence extends Riesel's generalization to three terms, not necessarily distinct, all base 2. Primes in this sequence begin 11, 13, 23, 37, 263, 277.
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LINKS
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Table of n, a(n) for n=1..38.
Eric W. Weisstein, "Generalized Fermat Number"
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FORMULA
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{(2^(2^a) + 1) + (2^(2^b) + 1) + (2^(2^c) + 1) = {A000215(a) + A000215(b) + A000215(c)}.
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EXAMPLE
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a(1) = 3 + 3 + 3 = 9. a(2) = 3 + 3 + 5 = 11. a(3) = 3 + 5 + 5 = 13. a(4) = 5 + 5 + 5 = 15. a(5) = 3 + 3 + 17 = 23. a(6) = 3 + 5 + 17 = 25. a(7) = 5 + 5 + 17 = 27. a(8) = 3 + 17 + 17 = 37. a(9) = 5 + 17 + 17 = 39. a(10) = 17 + 17 + 17 = 51. a(11) = 3 + 3 + 257 = 263.
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CROSSREFS
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Cf. A000215, A019434, A050922, A051179, A059919, A063486, A073617, A078303, A078304, A085866.
Sequence in context: A123760 A289686 A251394 * A214865 A225557 A120177
Adjacent sequences: A155874 A155875 A155876 * A155878 A155879 A155880
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post, Jan 29 2009
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EXTENSIONS
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More terms from R. J. Mathar, Feb 06 2009
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STATUS
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approved
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