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A067755 Even legs of Pythagorean triangles whose other leg and hypotenuse are both prime. 6
4, 12, 60, 180, 420, 1740, 1860, 2520, 3120, 5100, 8580, 9660, 16380, 19800, 36720, 60900, 71820, 83640, 100800, 106260, 135720, 161880, 163020, 199080, 205440, 218460, 273060, 282000, 337020, 388080, 431520, 491040, 531480, 539760, 552300 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Apart from the first two terms, every term is divisible by 60 and is of the form 450k^2+/-30k or 450k^2+/-330k+60 for some k.

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000

H. Dubner and T. Forbes, Prime Pythagorean triangles, J. Integer Seqs., Vol. 4 (2001), #01.2.3.

FORMULA

a(n) = (A048161(n)^2-1)/2 = A067756(n) - 1.

EXAMPLE

For p(1)=4, the right triangle 3, 4, 5 is the smallest with 3 and 5 prime. For p(10)=5100, the right triangle is 101, 5100, 5101 with 101 and 5101 prime.

MATHEMATICA

lst={}; Do[q=(Prime[n]^2+1)/2; If[PrimeQ[q], AppendTo[lst, (Prime[n]^2-1)/2]], {n, 200}]; lst (* Frank M Jackson, Nov 02 2013 *)

CROSSREFS

Cf. A048161, A067756.  Contains every value of A051858.

Sequence in context: A243923 A192331 A068525 * A051858 A084709 A057394

Adjacent sequences:  A067752 A067753 A067754 * A067756 A067757 A067758

KEYWORD

nonn

AUTHOR

Henry Bottomley, Jan 31 2002

STATUS

approved

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Last modified September 15 16:33 EDT 2019. Contains 327078 sequences. (Running on oeis4.)