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 A051859 Values of C (the hypotenuse) of a Pythagorean triangle with A (the short leg) and C both prime and part of a twin prime. 6
 5, 13, 61, 181, 421, 5101, 60901, 135721, 161881, 163021, 218461, 595141, 1108561, 2574181, 2740141, 3248701, 3535141, 3723721, 3729181, 8197201, 13933921, 20218441, 23605321, 28569241, 33874681, 47248921, 68667481, 69372421 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms of the sequence must be part of a Pythagorean triple of the form (2u-1), 2u*(u-1), (2u^2 - 2u + 1). - Joshua Zucker, May 12 2006 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA A051858 + 1, or 2*A051891^2 - 2*A051891 + 1, or 2*A051892^2 + 2*A051892 + 1. - Joshua Zucker, May 12 2006 MATHEMATICA tppQ[{a_, b_, c_}]:=AllTrue[{a, c}, PrimeQ]&&AnyTrue[a+{2, -2}, PrimeQ] && AnyTrue[ c+{2, -2}, PrimeQ]; Select[Table[{2n-1, 2n(n-1), 2n^2-2n+1}, {n, 2, 10000}], tppQ][[All, 3]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 27 2021 *) CROSSREFS See A051642 for the A's and A051858 for the B's. Subset of A067756. Sequence in context: A319249 A067756 A284035 * A151275 A149567 A149568 Adjacent sequences:  A051856 A051857 A051858 * A051860 A051861 A051862 KEYWORD nonn AUTHOR Stuart M. Ellerstein (ellerstein(AT)aol.com), Dec 14 1999 EXTENSIONS More terms from Joshua Zucker, May 12 2006 STATUS approved

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Last modified July 27 20:33 EDT 2021. Contains 346308 sequences. (Running on oeis4.)