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.

3, 5, 13, 85, 157, 12325, 12461, 106285, 276341, 339709, 10363909, 17238541, 1936511509, 51335823965, 133473142309, 872709007405, 1574530008629, 667511933218429, 698925273030725, 707670964169285, 1839944506840141

Offset

1,1

Comments

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

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..165 (first 100 terms from Lei Zhou)

Mathematica

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 *)
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 *)

Crossrefs

Cf. A018929, A018930.

Sequence in context: A159293 A051901 A268021 * A239381 A180313 A053630

Adjacent sequences: A018925 A018926 A018927 * A018929 A018930 A018931

Keyword

nonn

Author

Charles Reed (charles.reed(AT)bbs.ewgateway.org)

Extensions

More terms from David W. Wilson

Status

approved