login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A067834 Norm in ring Z[sqrt(3)] of (((-1+sqrt(3))^n)-1) is prime 0
2, 3, 7, 13, 19, 43, 61, 151, 257, 751, 859, 1453, 3767, 3889, 8171, 15959, 61961 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..17.

M. Oakes, Posting to primenumbers list on Feb 08 2002

FORMULA

(-2)^n-lucasV(-2, -2, n)+1, where lucasV(-2, -2, n) is the solution of the recurrence relation v[0]=2, v[1]=-2, v[n+2]=-2*v[n+1]+2*v[n] n >= 0.

EXAMPLE

a(2)=3 because (-2)^3-lucasV(-2,-2,3)+1 = -8-(-20)+1 = 13 and 13 is prime.

MATHEMATICA

v[0] = 2; v[1] = -2; v[n_] := v[n] = -2*v[n-1] + 2*v[n-2] ; s = {}; Do[If[PrimeQ[(-2)^n - v[n] + 1], Print[n]; AppendTo[s, n]], {n, 8171}]; s (* Jean-Fran├žois Alcover, Apr 18 2011 *)

CROSSREFS

Sequence in context: A249749 A171817 A156300 * A070754 A049887 A048216

Adjacent sequences:  A067831 A067832 A067833 * A067835 A067836 A067837

KEYWORD

easy,nice,nonn

AUTHOR

Mike Oakes, Feb 09 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 13:07 EST 2016. Contains 278875 sequences.