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 A099088 Indices of prime companion Pell numbers, divided by 2 (A001333). 5
 2, 3, 4, 5, 7, 8, 16, 19, 29, 47, 59, 163, 257, 421, 937, 947, 1493, 1901, 6689, 8087, 9679, 28753, 79043, 129127, 145969, 165799, 168677, 170413, 172243 (list; graph; refs; listen; history; text; internal format)
 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 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 Do[If[PrimeQ[Expand[((1 + Sqrt[2])^n + (1 - Sqrt[2])^n)/2]], Print[n]], {n, 0, 1000}] (* Artur Jasinski, Dec 10 2006 *) CROSSREFS Cf. A002203 (companion Pell numbers), A086395 (primes in A001333), A096650 (indices of prime Pell numbers). Cf. A005850. Sequence in context: A039088 A111794 A030290 * A029447 A212317 A161751 Adjacent sequences:  A099085 A099086 A099087 * A099089 A099090 A099091 KEYWORD hard,nonn AUTHOR T. D. Noe, Sep 24 2004 EXTENSIONS a(24) = 129127 from Eric W. Weisstein, May 22 2006 a(25) = 145969 from Eric W. Weisstein, Aug 29 2006 a(26) = 165799 from Eric W. Weisstein, Nov 11 2006 a(27) = 168677 from Eric W. Weisstein, Nov 26 2006 a(28) = 170413 from Eric W. Weisstein, Dec 10 2006 a(29) = 172243 from Eric W. Weisstein, Jan 25 2007 STATUS approved

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