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 A155185 Primes in A155175. 2
 5, 13, 113, 1741, 5101, 8581, 9941, 21841, 26681, 47741, 82013, 481181, 501001, 1009621, 2356621, 2542513, 3279361, 3723721, 4277813, 7757861, 8124481, 13204661, 25311613, 30772013, 44170601, 48619661, 51521401, 52541501, 54236113, 60731221, 72902813 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Hypotenuse C (prime numbers only) of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes. p=1,q=2,a=3,b=4,c=5=prime,s=12-+1primes, ... LINKS MATHEMATICA lst={}; Do[p=n; q=p+1; a=q^2-p^2; c=q^2+p^2; b=2*p*q; ar=a*b/2; s=a+b+c; If[PrimeQ[s-1]&&PrimeQ[s+1], If[PrimeQ[c], AppendTo[lst, c]]], {n, 8!}]; lst (* corrected by Ray Chandler, Feb 11 2020 *) CROSSREFS Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589 Sequence in context: A117527 A228280 A155175 * A213129 A004063 A005764 Adjacent sequences:  A155182 A155183 A155184 * A155186 A155187 A155188 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Jan 21 2009 EXTENSIONS Sequence corrected by Ray Chandler, Feb 11 2020 STATUS approved

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Last modified May 16 12:46 EDT 2021. Contains 343947 sequences. (Running on oeis4.)