A132404 Smallest short legs 'A' of exactly n primitive Pythagorean triangles.

3, 20, 60, 204, 5040, 420, 660, 2040

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 26 2008

Keywords

• nonn
• more

Comments

Where records occur in A024359. a(12) = 13860, a(13) = 4620, and a(14) = 7140. - T. D. Noe, Feb 23 2012

From Colin Barker, Oct 25 2015: (Start)

a(11) = 872100, a(15) = 22440 and a(16) = 55440.

a(9), a(10), a(17), a(18), a(19) and a(20) are not less than 6000000.

(End)

Examples

			The solutions for the first 7 are
1, (3,4,5)
2, (20,21,29), (20,99,101)
3, (60,91,109), (60,221,229), (60,899,901)
4, (204,253,325), (204,1147,1165), (204,2597,2605), (204,10403,10405)
5, (5040,78319,78481), (5040,99161,99289), (5040,129551,129649), (5040,253991,254041), (5040,6350399,6350401)
6, (420,851,949), (420,1189,1261), (420,1739,1789), (420,4891,4909), (420,11021,11029), (420,44099,44101)
7, (660,779,1021), (660,989,1189), (660,2989,3061), (660,4331,4381), (660,12091,12109), (660,27221,27229), (660,108899,108901)
		

Crossrefs

Cf. A024359.

Programs

Mathematica

PyphagoreanAs[a_] := (q={}; k=0; If[a>=8,r=4,r=1]; Do[y=(a^2+b^2)^0.5; c=IntegerPart[y]; If[c==y, p=0; If[GCD[a,b,c]==1, AppendTo[q,a.b.c]; k++ ]], {b,a+1,a^2/r}]; PrependTo[q,k]; q); lst={}; x=0; Do[w=PyphagoreanAs[n][[1]]; If[w>x, Print[Date[],"A=",n,",w=",w]; AppendTo[lst,n]; x=w], {n,1000}]; lst
solns[a_] := Module[{b, c, soln}, soln = Reduce[a^2 + b^2 == c^2 && a < b && c > 0 && GCD[a, b, c] == 1, {b, c}, Integers]; If[soln === False, 0, If[soln[[1, 1]] === b, 1, Length[soln]]]]; nn = 20; t = Table[0, {nn}]; Do[s = solns[n]; If[s > nn, Print[{s, n}], If[t[[s]] == 0, t[[s]] = n; Print[{s, n}]]], {n, 5040}]; t (* T. D. Noe, Feb 23 2012 *)

Extensions

a(5) from T. D. Noe, Feb 23 2012