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A155180 Short leg A of primitive Pythagorean triangles such that perimeters and products of 3 sides 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, pr=a*b*c, pr-+1 are primes. 3
3, 15833, 71765, 75633, 94983, 256859, 263661, 292943, 309599, 315159, 340439, 349929, 375089, 415659, 416079, 445775, 446285, 525005, 583089, 639651, 655205, 663255, 707715, 953363, 955319, 988415, 1044051, 1074909, 1081365, 1116323 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

p=1,q=2,a=3,b=4,c=5,s=12-+1 primes,pr=3*4*5=60-+1 primes, ...

LINKS

Table of n, a(n) for n=1..30.

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; pr=a*b*c; If[PrimeQ[s-1]&&PrimeQ[s+1]&&PrimeQ[pr-1]&&PrimeQ[pr+1], AppendTo[lst, a]], {n, 3*9!}]; lst

CROSSREFS

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178

Sequence in context: A195834 A124393 A116182 * A182914 A203182 A128121

Adjacent sequences:  A155177 A155178 A155179 * A155181 A155182 A155183

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)