cp's OEIS Frontend

A306120 Lengths of largest face diagonal in primitive Euler bricks or Pythagorean cuboids: possible values of max(d, e, f) for solutions to a^2 + b^2 = d^2, a^2 + c^2 = e^2, b^2 + c^2 = f^2 in coprime positive integers a, b, c, d, e, f.

%I A306120 #16 Dec 06 2024 16:31:09
%S A306120 267,373,732,825,843,1595,1884,2500,2775,3725,3883,6380,6409,8140,
%T A306120 8579,9188,9272,9512,11764,12125,13123,14547,14681,14701,19572,20503,
%U A306120 20652,24695,25121,25724,29307,30032,30695,31080,32595,34484,37104,37895,38201,38965
%N A306120 Lengths of largest face diagonal in primitive Euler bricks or Pythagorean cuboids: possible values of max(d, e, f) for solutions to a^2 + b^2 = d^2, a^2 + c^2 = e^2, b^2 + c^2 = f^2 in coprime positive integers a, b, c, d, e, f.
%C A306120 These are the values obtained as sqrt(A031173(n)^2 + A031174(n)^2), sorted by size (n = 3 yields 843, n = 4 yields 732) and duplicates removed: The first duplicate is 71402500^2 = A031173(1428)^2 + A031174(1428)^2 = A031173(1626)^2 + A031174(1626)^2, there is no other among the first 3500 terms.
%C A306120 This considers only the face diagonals, not the space diagonals.
%C A306120 See the main entry A031173 for links, cross-references, and further comments.
%H A306120 M. F. Hasler, <a href="/A306120/b306120.txt">Table of n, a(n) for n = 1..2500</a>
%F A306120 A306120 = { sqrtint(A031173(n)^2+A031174(n)^2); n >= 1 }.
%o A306120 (PARI) A306120=Set(vector(1000,n,sqrtint(A031173(n)^2+A031174(n)^2)))[1..-100] \\ Discard the last 100 values, which may have holes. This is empirical: better find the smallest sqrtint(A031173(n)^2+A031174(n)^2) with n > 1000 not in the set, and discard all elements larger than that.
%Y A306120 Cf. A031173, A031174, A031175, A195816, A196943, A268396.
%K A306120 nonn
%O A306120 1,1
%A A306120 _M. F. Hasler_, Oct 11 2018