cp's OEIS Frontend

A018928 Define {b(n)} by b(1)=3, b(n) (n >= 2) is the smallest number such that b(1)^2 + ... + b(n)^2 = m^2 for some m and all b(i) are distinct. Sequence gives values of m.

%I A018928 #37 Nov 04 2023 06:31:06
%S A018928 3,5,13,85,157,12325,12461,106285,276341,339709,10363909,17238541,
%T A018928 1936511509,51335823965,133473142309,872709007405,1574530008629,
%U A018928 667511933218429,698925273030725,707670964169285,1839944506840141
%N A018928 Define {b(n)} by b(1)=3, b(n) (n >= 2) is the smallest number such that b(1)^2 + ... + b(n)^2 = m^2 for some m and all b(i) are distinct. Sequence gives values of m.
%C A018928 Also: Begin with the least length of a Pythagorean Triangle (PT), a(1)=3. Then a(n) is the least hypotenuse of a PT which has a(n-1) as one of its legs. - _Robert G. Wilson v_, Mar 17 2014
%H A018928 Robert G. Wilson v, <a href="/A018928/b018928.txt">Table of n, a(n) for n = 1..165</a> (first 100 terms from Lei Zhou)
%t A018928 NextA018928[n_] := Block[{a = n^2, b, l, i, c, d, f}, b = Divisors[a]; l = Length[b]; i = l; While[i--; c = b[[i]]; d = a/c - (c - 1); (d <= 1) || EvenQ[d]]; f = (a/c + (c - 1) + 1)/2]; Table[If[i == 1, a = 3, a = NextA018928[a]]; a, {i, 1, 21}](* _Lei Zhou_, Feb 20 2014 *)
%t A018928 f[s_List] := Block[{x = s[[-1]]}, Append[s, Transpose[ Solve[ x^2 + y^2 == z^2 && y > 0 && z > 0, {y, z}, Integers]][[-1, 1, 2]]]]; lst = Nest[f, lst, 15] (* _Robert G. Wilson v_, Mar 17 2014 *)
%Y A018928 Cf. A018929, A018930.
%K A018928 nonn
%O A018928 1,1
%A A018928 Charles Reed (charles.reed(AT)bbs.ewgateway.org)
%E A018928 More terms from _David W. Wilson_