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A132404
Smallest short legs 'A' of exactly n primitive Pythagorean triangles.
2
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)
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
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(5) from T. D. Noe, Feb 23 2012
STATUS
approved