|
Search: id:A085153
|
|
|
| A085153 |
|
Sequence related to ABC conjecture: all prime factors of n and n+1 are <= 7. |
|
+0
5
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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
|
|
LINKS
|
A. Nitaj, The ABC conjecture homepage
|
|
MATHEMATICA
|
Select[Range[10000], FactorInteger[ # (# + 1)][[ -1, 1]] <= 7 &] - T. D. Noe (noe(AT)sspectra.com), Mar 03 2008
|
|
CROSSREFS
|
Cf. A085152, A002473, A086247.
Adjacent sequences: A085150 A085151 A085152 this_sequence A085154 A085155 A085156
Sequence in context: A092597 A125506 A079334 this_sequence A130010 A033081 A032579
|
|
KEYWORD
|
nonn,fini,full
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2003
|
|
EXTENSIONS
|
Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Jun 30 2003
|
|
|
Search completed in 0.002 seconds
|
