A385022 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A002378(n) and its long leg and hypotenuse are consecutive natural numbers.

3, 4, 5, 11, 60, 61, 23, 264, 265, 39, 760, 761, 59, 1740, 1741, 83, 3444, 3445, 111, 6160, 6161, 143, 10224, 10225, 179, 16020, 16021, 219, 23980, 23981, 263, 34584, 34585, 311, 48360, 48361, 363, 65884, 65885, 419, 87780, 87781, 479, 114720, 114721, 543, 147424, 147425

Offset

1,1

Links

Table of n, a(n) for n=1..48.

José Miguel Blanco Casado and Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas

Formula

row(n) = (2*T(n) - 1, 2*T(n)*(T(n) - 1), 2*T(n)*(T(n) - 1) + 1) where T(n) = A002378(n).

Example

  n=1:      3,     4,     5;
  n=2:     11,    60,    61;
  n=3:     23,   264,   265;
  ...

Mathematica

a=Table[(n(n+1)), {n, 1, 16}]; Apply[Join, Map[{2#-1, 2#^2-2#, 2#^2-2#+1}&, a]]

Crossrefs

Cf. A002378, A142463 (short leg), A385187 (area).

Sequence in context: A341785 A052276 A173096 * A378395 A302752 A046964

Adjacent sequences: A385019 A385020 A385021 * A385023 A385024 A385025

Keyword

sign,easy,tabf

Author

Miguel-Ángel Pérez García-Ortega, Jun 15 2025

Status

approved