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A099088
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Indices of prime companion Pell numbers, divided by 2 (A001333).
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 (grafix(AT)csl.pl), Dec 10 2006
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LINKS
| Eric Weisstein's World of Mathematics, Pell Number
Eric Weisstein's World of Mathematics, Integer Sequence Primes
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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 (grafix(AT)csl.pl), Dec 10 2006
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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 A161751 A105362
Adjacent sequences: A099085 A099086 A099087 * A099089 A099090 A099091
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KEYWORD
| hard,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Sep 24 2004
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EXTENSIONS
| a(24) = 129127 from Eric Weisstein (eric(AT)weisstein.com), May 22, 2006
a(25) = 145969 from Eric Weisstein (eric(AT)weisstein.com), Aug 29, 2006
a(26) = 165799 from Eric Weisstein (eric(AT)weisstein.com), Nov 11, 2006
a(27) = 168677 from Eric Weisstein (eric(AT)weisstein.com), Nov 26, 2006
a(28) = 170413 from Eric Weisstein (eric(AT)weisstein.com), Dec 10, 2006
a(29) = 172243 from Eric Weisstein (eric(AT)weisstein.com), Jan 25, 2007
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