|
Search: id:A129743
|
|
|
| A129743 |
|
a(n) = -(u^n-1)*(v^n-1) with u = 2+sqrt(3), v = 2-sqrt(3). |
|
+0
2
|
|
| 2, 12, 50, 192, 722, 2700, 10082, 37632, 140450, 524172, 1956242, 7300800, 27246962, 101687052, 379501250, 1416317952, 5285770562, 19726764300, 73621286642, 274758382272, 1025412242450, 3826890587532, 14282150107682
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Each term of this sequence beyond the sixth has a primitive prime divisor. - Anthony Flatters (Anthony.Flatters(AT)uea.ac.uk), Aug 17 2007
|
|
REFERENCES
|
G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
|
|
LINKS
|
Anthony Flatters, Primitive Divisors of some Lehmer-Pierce Sequences, arXiv:0708.2190.
|
|
FORMULA
|
a(2*n) = 12*A001353(n)^2, a(2*n+1) =2*A001834(n)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2007
Equals 2*A092184(n). - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 04 2007.
O.g.f.: 2*x*(1+x)/((1-x)*(1-4*x+x^2)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
|
|
MAPLE
|
u:=2+sqrt(3): v:=2-sqrt(3): a:=n->expand(-(u^n-1)*(v^n-1)): seq(a(n), n=1..28); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2007
|
|
MATHEMATICA
|
Table[Simplify[ -((2 + Sqrt[3])^n - 1)*((2 - Sqrt[3])^n - 1)], {n, 1, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 15 2007
|
|
CROSSREFS
|
Sequence in context: A039784 A028243 A003493 this_sequence A115243 A012423 A012427
Adjacent sequences: A129740 A129741 A129742 this_sequence A129744 A129745 A129746
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), May 13 2007
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 13 2007
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2007
|
|
|
Search completed in 0.002 seconds
|
