OFFSET
1,1
COMMENTS
Note that for A001333(n) to be prime, the index n must be prime or a power of 2. The indices greater than 421 yield probable primes.
Numbers n for which ((1+sqrt(2))^n + (1-sqrt(2))^n)/2 is prime. - Artur Jasinski, Dec 10 2006
REFERENCES
F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 62, 1983.
LINKS
J. B. Cosgrave and K. Dilcher, Pairs of reciprocal quadratic congruences involving primes, Fib. Quart. 51 (2) (2013) 98, after Theorem 3.
Eric Weisstein's World of Mathematics, Pell Number
Eric Weisstein's World of Mathematics, Integer Sequence Primes
MATHEMATICA
lst={}; a=1; b=1; Do[c=a+2b; a=b; b=c; If[PrimeQ[c], AppendTo[lst, n]], {n, 2, 10000}]; lst
(* Second program: *)
Do[If[PrimeQ[Expand[((1 + Sqrt[2])^n + (1 - Sqrt[2])^n)/2]], Print[n]], {n, 0, 1000}] (* Artur Jasinski, Dec 10 2006 *)
PROG
(PARI) isok(n) = isprime(polchebyshev(n, 1, I)/I^n); \\ Michel Marcus, Dec 07 2018
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, Sep 24 2004
EXTENSIONS
a(24) from Eric W. Weisstein, May 22 2006
a(25) from Eric W. Weisstein, Aug 29 2006
a(26) from Eric W. Weisstein, Nov 11 2006
a(27) from Eric W. Weisstein, Nov 26 2006
a(28) from Eric W. Weisstein, Dec 10 2006
a(29) from Eric W. Weisstein, Jan 25 2007
a(30) from Robert Price, Dec 07 2018
a(31) from Robert Price, Dec 05 2023
STATUS
approved