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
KEYWORD
nonn,more
AUTHOR
Vladimir Joseph Stephan Orlovsky, Aug 26 2008
EXTENSIONS
a(5) from T. D. Noe, Feb 23 2012
STATUS
approved