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 A056869 Prime hypotenuses of Pythagorean triangles with consecutive integer sides. 3
 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449, 4760981394323203445293052612223893281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These primes belong to A001653. From Jianing Song, Jan 02 2019: (Start) Essentially the same sequence as A086383. If p is a term then it is a unique-period prime in base sqrt(2*p^2 - 1). (End) LINKS Robert Israel, Table of n, a(n) for n = 1..22 FORMULA a(n) = A086383(n+1). - Jianing Song, Jan 02 2019 EXAMPLE 29 is included because it is prime and it is the hypotenuse of the 20, 21, 29 Pythagorean triangle. MAPLE f:= gfun:-rectoproc({a(n)=6*a(n-1)-a(n-2), a(1)=1, a(2)=5}, a(n), remember): select(isprime, [seq(f(n), n=1..1000)]); # Robert Israel, Oct 13 2015 MATHEMATICA Select[Sqrt[#^2+(#+1)^2]&/@With[{p=3+2Sqrt[2]}, NestList[Floor[p #]+3&, 3, 120]], PrimeQ] (* Harvey P. Dale, May 02 2018 *) PROG (PARI) t(n) = if(n<3, 5^(n-1), 6*t(n-1)-t(n-2)); for(n=1, 50, if(isprime(t(n)), print1(t(n)", "))) \\ Altug Alkan, Oct 13 2015 (GAP) f:=[1, 5];; for n in [3..60] do f[n]:=6*f[n-1]-f[n-2]; od; a:=Filtered(f, IsPrime);; Print(a); # Muniru A Asiru, Jan 03 2019 CROSSREFS Cf. A000129, A001653, A001652, A046090, A086383. Sequence in context: A057705 A237188 A086720 * A228028 A237256 A172041 Adjacent sequences:  A056866 A056867 A056868 * A056870 A056871 A056872 KEYWORD nonn AUTHOR Harvey P. Dale, Sep 02 2000 EXTENSIONS Incorrect link to index entries for linear recurrences with constant coefficients removed by Colin Barker, Oct 13 2015 Offset changed to 1 by Colin Barker, Oct 13 2015 STATUS approved

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Last modified April 18 05:11 EDT 2021. Contains 343072 sequences. (Running on oeis4.)