|
Search: id:A155180
|
|
|
| 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. |
|
+0
5
|
|
| 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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
p=1,q=2,a=3,b=4,c=5,s=12-+1 primes,pr=3*4*5=60-+1 primes, ...
|
|
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: A047777 A124393 A116182 this_sequence A128121 A112406 A115475
Adjacent sequences: A155177 A155178 A155179 this_sequence A155181 A155182 A155183
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 21 2009
|
|
|
Search completed in 0.006 seconds
|
