STATUS
reviewed
approved
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reviewed
approved
proposed
reviewed
editing
proposed
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 *)
Sequence corrected after second term and program corrected by Ray Chandler, Feb 11 2020
proposed
editing
editing
proposed
5, 13, 841, 113, 1741, 3961, 5101, 8581, 276025, 289561, 711625, 2906461, 3545785, 9941, 21841, 26681, 47741, 82013, 481181, 501001, 1009621, 2356621, 2542513, 3279361, 3723721, 4533061, 5187421, 5284501, 5947801, 11286001, 19052965, 21773401, 23344945, 26129221, 37575781, 41032741, 43459165, 45324721, 472294814277813, 7757861, 8124481, 13204661, 25311613, 30772013, 44170601, 48619661, 51521401, 52541501, 54236113, 60731221, 72902813
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[ac], AppendTo[lst, c]]], {n, 8!}]; lst
Sequence corrected after second term and program corrected by Ray Chandler, Feb 11 2020
approved
editing
_Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), _, Jan 21 2009
Primes in A155175.
5, 13, 841, 1741, 3961, 5101, 8581, 276025, 289561, 711625, 2906461, 3545785, 3723721, 4533061, 5187421, 5284501, 5947801, 11286001, 19052965, 21773401, 23344945, 26129221, 37575781, 41032741, 43459165, 45324721, 47229481
1,1
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, ...
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[a], AppendTo[lst, c]]], {n, 8!}]; lst
nonn
Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 21 2009
approved