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A099088
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Indices of prime companion Pell numbers, divided by 2 (A001333).
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7
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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
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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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Table of n, a(n) for n=1..30.
Eric Weisstein's World of Mathematics, Pell Number
Eric Weisstein's World of Mathematics, Integer Sequence Primes
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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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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
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KEYWORD
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hard,nonn
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AUTHOR
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T. D. Noe, Sep 24 2004
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EXTENSIONS
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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
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STATUS
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approved
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