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Search: id:A002760
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| 0, 1, 4, 8, 9, 16, 25, 27, 36, 49, 64, 81, 100, 121, 125, 144, 169, 196, 216, 225, 256, 289, 324, 343, 361, 400, 441, 484, 512, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1000, 1024, 1089, 1156, 1225, 1296, 1331
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OFFSET
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1,3
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COMMENT
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Catalan's Conjecture states that 8 and 9 are the only pair of consecutive numbers in this sequence. The conjecture was established in 2003 by Mihilescu.
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REFERENCES
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Bilu, Y. F., Catalan's Conjecture (After Mihilescu). Asterisque, No. 294, 1-26, 2004.
Bilu, Y. F., Catalan Without Logarithmic Forms (after Bugeaud, Hanrot and Mihilescu). J. Theor. Nombres Bordeaux 17, 69-85, 2005.
Metsankyla, T., Catalan's Conjecture: Another Old Diophantine Problem Solved. Bull. Amer. Math. Soc. 41, 43-57, 2003.
Mihilescu, P., A Class Number Free Criterion for Catalan's Conjecture. J. Number Th. 99 225-231, 2003.
Mihilescu, P., Primary Cyclotomic Units and a Proof of Catalan's Conjecture. J. Reine Angew. Math. 572, 167-195, 2004.
P. Ribenboim, Catalan's conjecture, Amer. Math. Monthly, 103 (1996), 529-538.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 68.
C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 236.
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..1000.
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CROSSREFS
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Cf. A131799; union of A000290 and A000578.
Sequence in context: A134612 A025475 A125643 this_sequence A115651 A062559 A010417
Adjacent sequences: A002757 A002758 A002759 this_sequence A002761 A002762 A002763
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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