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A099088
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Indices of prime companion Pell numbers, divided by 2 (A001333).
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8
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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, 278321, 552283
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 62, 1983.
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(PARI) isok(n) = isprime(polchebyshev(n, 1, I)/I^n); \\ Michel Marcus, Dec 07 2018
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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