The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A165236 Short legs of primitive Pythagorean Triples (a,b,c) such that 2*a+1, 2*b+1 and 2*c+1 are primes. 3
 20, 33, 44, 56, 68, 273, 303, 320, 380, 440, 483, 740, 1071, 1089, 1101, 1220, 1376, 1484, 1635, 1773, 1808, 1869, 1940, 1965, 2000, 2120, 2144, 2204, 2319, 2715, 2763, 3003, 3164, 3309, 3500, 3603, 3729, 3740, 3753, 3801, 4148, 4215, 4323, 4340, 4401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Only one instance of a enters the sequence if multiple solutions exist, like with (a,b,c) = (320,999,1049) and (a,b,c) = (320,25599,25601). Subsequence of A009004. [R. J. Mathar, Mar 25 2010] LINKS Table of n, a(n) for n=1..45. EXAMPLE (a,b,c) = (20,21,29), (33,56,65), (44,483,485), (56,783,785), (68,285,293), (273,4136,4145). In the first case, for example, 2*20+1=41, 2*21+1 and 2*29+1 are all prime, which adds the half-leg 20 to the sequence. MATHEMATICA amax=6*10^4; lst={}; k=0; q=12!; Do[If[(e=((n+1)^2-n^2))>amax, Break[]]; Do[If[GCD[m, n]==1, a=m^2-n^2; If[PrimeQ[2*a+1], b=2*m*n; If[PrimeQ[2*b+1], If[GCD[a, b]==1, If[a>b, {a, b}={b, a}]; If[a>amax, Break[]]; c=m^2+n^2; If[PrimeQ[2*c+1], k++; AppendTo[lst, a]]]]]]; If[a>amax, Break[]], {m, n+1, 12!, 2}], {n, 1, q, 1}]; Union@lst CROSSREFS Cf. A009004, A020883, A165237, A165238 Sequence in context: A119873 A364307 A075230 * A067468 A127906 A108667 Adjacent sequences: A165233 A165234 A165235 * A165237 A165238 A165239 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Sep 09 2009 EXTENSIONS Comments moved to examples and definition clarified by R. J. Mathar, Mar 25 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)