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A155178 Numbers p 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. 4
1, 7916, 35882, 37816, 47491, 128429, 131830, 146471, 154799, 157579, 170219, 174964, 187544, 207829, 208039, 222887, 223142, 262502, 291544, 319825, 327602, 331627, 353857, 476681, 477659, 494207, 522025, 537454, 540682, 558161, 571670 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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..31.

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, n]], {n, 3*9!}]; lst

CROSSREFS

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

Sequence in context: A237969 A256163 A171111 * A031922 A121236 A233976

Adjacent sequences: A155175 A155176 A155177 * A155179 A155180 A155181

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

STATUS

approved

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Last modified November 29 09:23 EST 2022. Contains 358422 sequences. (Running on oeis4.)