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 A365796 Sequence of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its short leg the hypotenuse of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers. 3
 3, 4, 5, 5, 12, 13, 13, 84, 85, 85, 3612, 3613, 3613, 6526884, 6526885, 6526885, 21300113901612, 21300113901613, 21300113901613, 226847426110843688722000884, 226847426110843688722000885, 226847426110843688722000885, 25729877366557343481074291996721923093306518970391612 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See Corolario 5.1.1. of the reference file (first section). (a_1, b_1, c_1) = (3,4,5) and for each n > 1: (a_n, b_n, c_n) = (c_(n-1), (c_(n-1))^2-1)/2, ((c_(n-1))^2+1)/2). REFERENCES J. M. Blanco Casado, J. M. Sánchez Muñoz, and M. A. Pérez García-Ortega, El Libro de las Ternas Pitagóricas, Preprint 2023. LINKS Table of n, a(n) for n=1..23. Miguel-Ángel Pérez García-Ortega, Capitulo 5. Catetos, El Libro de las Ternas Pitagóricas. EXAMPLE Triples begin: 3, 4, 5; 5, 12, 13; 13, 84, 85; 85, 3612, 3613; ... MATHEMATICA {a0, b0, c0}={3, 4, 5}; m=8; f[n_]:=Module[{fn0=c0, fn1=(c0^2+1)/2}, Do[{fn0, fn1}={fn1, (fn0^2+1)/2}, {2n-1}]; fn0]; t[n_]:={f[n-1], f[n]-1, f[n]}; ternas={a0, b0, c0}; For[i=1, i<=m, i++, ternas=Join[ternas, t[i]]]; ternas CROSSREFS Cf. A007018 (inradius), A000058 (lower exinradius). Cf. A053631 (long leg), A053630 (hypotenuse), A365577, A365578. Sequence in context: A103606 A139794 A369493 * A202819 A185383 A004484 Adjacent sequences: A365793 A365794 A365795 * A365797 A365798 A365799 KEYWORD nonn,tabf,more AUTHOR Miguel-Ángel Pérez García-Ortega, Sep 19 2023 STATUS approved

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Last modified May 26 16:43 EDT 2024. Contains 372840 sequences. (Running on oeis4.)