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A085153
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Sequence related to ABC conjecture: all prime factors of n and n+1 are <= 7.
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22
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1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 20, 24, 27, 35, 48, 49, 63, 80, 125, 224, 2400, 4374
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The ABC conjecture would imply that if the prime factors of A, B, C are prescribed in advance, then there is only a finite number of solutions to the equation A + B = C with gcd(A,B,C)=1 (indeed it would bound C to be no more than "roughly" the product of those primes). So in particular there ought to be only finitely many pairs of adjacent integers whose prime factors are limited to {2, 3, 5, 7} (D. Rusin).
This sequence is complete by a theorem of Stormer. See A002071. - T. D. Noe (noe(AT)sspectra.com), Mar 03 2008
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LINKS
| A. Nitaj, The ABC conjecture homepage
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MATHEMATICA
| Select[Range[10000], FactorInteger[ # (# + 1)][[ -1, 1]] <= 7 &] - T. D. Noe (noe(AT)sspectra.com), Mar 03 2008
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CROSSREFS
| Cf. A085152, A002473, A086247.
Sequence in context: A092597 A125506 A079334 * A130010 A033081 A032579
Adjacent sequences: A085150 A085151 A085152 * A085154 A085155 A085156
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KEYWORD
| nonn,fini,full
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2003
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jun 30 2003
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