|
Search: id:A031433
|
|
|
| A031433 |
|
Least term in period of continued fraction for sqrt(n) is 9. |
|
+0
5
|
|
| 83, 328, 735, 1304, 2035, 2928, 3983, 5200, 6579, 7415, 8120, 9235, 9823, 11688, 13715, 15904, 17190, 18255, 20768, 23443, 23750, 26280, 26605, 29279, 29622, 31015, 32440, 35763, 39248, 42895, 45416, 46704, 48890, 50675, 54808, 59103
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
a(n)=81*n^2+2*n (n>0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 01 2009]
If A=[A031433] 81*n.^2+2*n (83,328,735,.,); Y=[A157505] 1458*n+18 (1476,2934,4392, 5850..,); X=[A157506] 13122*n^2+324*n+1 (13447,53137,119071,...), we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 13447^2-83*1476^2=1; 53137^2-328*2934^2=1; 119071^2-735*4392^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 02 2009]
If A=[A031433] 81*n.^2+2*n (n>0, 83, 328, 735,.,. ,.,); Y=[A010734] 9 (9,9,9,.,..,); X=[A158123] 81*n+1 (n>0, 82, 163, 244, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 82^2-83*9^2=1; 163^2-328*9^2=1; 244^2-735*9^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
|
|
LINKS
|
Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 01 2009]
Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 02 2009]
|
|
CROSSREFS
|
Cf. A157505, A157506 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 02 2009]
Cf. A010734, A158123 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
Sequence in context: A142387 A145651 A141570 this_sequence A061525 A160359 A142496
Adjacent sequences: A031430 A031431 A031432 this_sequence A031434 A031435 A031436
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
David W. Wilson (davidwwilson(AT)comcast.net)
|
|
|
Search completed in 0.002 seconds
|
