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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, p+1=q(prime), 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. 0
2, 3, 11, 71, 227, 491, 683, 1103, 1187, 2591, 3923, 4271, 4931, 6737, 7193, 7703, 8093, 8753, 8963, 9173, 9377, 10271, 13043, 13451, 13997, 15233, 15443, 15803, 15887, 17957, 18701, 19961, 20681, 21701, 22031, 22073, 24371, 24473, 24683 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

p=1,q=2(prime),a=3,b=4,c=5,s=12-+1 primes, ...

LINKS

Table of n, a(n) for n=1..39.

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[q], AppendTo[lst, q]]], {n, 8!}]; lst

CROSSREFS

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150, A155186, A068231, A129517, A054574, A132281

Sequence in context: A184310 A301347 A241811 * A109132 A279084 A008510

Adjacent sequences:  A155184 A155185 A155186 * A155188 A155189 A155190

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

STATUS

approved

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)