A101903 Number of twin Pythagorean triples with hypotenuse less than 10^n.

1, 7, 24, 74, 228, 712, 2243, 7079, 22370, 70722, 223619, 707120, 2236083, 7071084, 22360697, 70710696, 223606818, 707106802, 2236067999, 7071067836, 22360679800, 70710678145, 223606797778, 707106781216, 2236067977530

Offset

1,2

Comments

a(n) <= 10^(n/2)/sqrt(2). - Robert G. Wilson v, Jan 08 2005

Links

Table of n, a(n) for n=1..25.

Ravi P. Agarwal, Pythagorean Triples Before and after Pythagoras, Computation 2020, 8(3), 62, p. 14.

Eric Weisstein's World of Mathematics, Twin Pythagorean Triple

Example

For a(2)=7 because {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {20, 21, 29}, {9, 40, 41}, {11, 60, 61}, {13, 84, 85}.

Mathematica

f[n_] := Round[ Sqrt[ (10^n - 1)/2] - 1]; a[n_] := (MatrixPower[{{1, 2, 2}, {2, 1, 2}, {2, 2, 3}}, n].{{1}, {0}, {1}})[[3, 1]]; t = Table[ a[n], {n, 2, 35}]; g[n_] := Length[ Select[t, # < 10^n &]]; Table[f[n] + g[n], {n, 25}] (* Robert G. Wilson v, Jan 08 2005 *)

Crossrefs

Sequence in context: A211381 A339254 A305676 * A212504 A196349 A196352

Adjacent sequences: A101900 A101901 A101902 * A101904 A101905 A101906

Keyword

nonn

Author

Eric W. Weisstein, Dec 20 2004

Extensions

a(5) and up from Robert G. Wilson v, Jan 08 2005

Status

approved