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

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

Offset

1,1

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)

Links

Table of n, a(n) for n=1..8.

Example

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)

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 *)

Crossrefs

Cf. A024359.

Sequence in context: A360417 A281268 A143582 * A062359 A342672 A099721

Adjacent sequences: A132401 A132402 A132403 * A132405 A132406 A132407

Keyword

nonn,more

Author

Vladimir Joseph Stephan Orlovsky, Aug 26 2008

Extensions

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

Status

approved