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A086383
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Prime terms in the sequence of Pell numbers, A000129.
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9
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2, 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449, 4760981394323203445293052612223893281
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OFFSET
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1,1
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COMMENTS
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Previous Name: Primes found among the denominators of the continued fraction rational approximations to sqrt(2).
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LINKS
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FORMULA
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EXAMPLE
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MATHEMATICA
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Select[Table[ChebyshevU[k, 3]-ChebyshevU[k-1, 3], {k, 0, 50}], PrimeQ] (* Ed Pegg Jr, May 10 2007 *)
Select[Denominator[Convergents[Sqrt[2], 150]], PrimeQ] (* Harvey P. Dale, Dec 19 2012 *)
Select[LinearRecurrence[{2, 1}, {0, 1}, 16], PrimeQ] (* Zak Seidov, Oct 21 2013 *)
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PROG
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(PARI) \\ Continued fraction rational approximation of numeric constants f. m=steps.
cfracdenomprime(m, f) = { default(realprecision, 3000); cf = vector(m+10); x=f; for(n=0, m, i=floor(x); x=1/(x-i); cf[n+1] = i; ); for(m1=0, m, r=cf[m1+1]; forstep(n=m1, 1, -1, r = 1/r; r+=cf[n]; ); numer=numerator(r); denom=denominator(r); if(ispseudoprime(denom), print1(denom, ", ")); ) }
(GAP) f:=[0, 1];; for n in [3..100] do f[n]:=2*f[n-1]+f[n-2]; od; a:=Filtered(f, IsPrime);; Print(a); # Muniru A Asiru, Jan 03 2019
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CROSSREFS
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KEYWORD
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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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