cp's OEIS Frontend

A198455 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = 1, ordered by a and then b; sequence gives b values.

%I A198455 #28 Feb 16 2025 21:25:21
%S A198455 2,5,9,6,14,9,20,27,10,35,13,21,44,26,54,14,20,65,17,24,77,44,90,14,
%T A198455 18,33,51,104,21,38,119,135,22,49,75,152,25,55,84,170,35,45,189,26,39,
%U A198455 50,68,209,29,35,75,114,230,125
%N A198455 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 1, ordered by a and then b; sequence gives b values.
%C A198455 See A198453.
%C A198455 The definition amounts to saying that T_a+T_b=T_c where T_i denotes a triangular number (A000217). - _N. J. A. Sloane_, Apr 01 2020
%D A198455 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198455 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%H A198455 J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, <a href="http://arxiv.org/abs/2004.14000">Three Cousins of Recaman's Sequence</a>, arXiv:2004:14000 [math.NT], April 2020.
%e A198455 2*3 + 2*3 = 3*4
%e A198455 3*4 + 5*6 = 6*7
%e A198455 4*5 + 9*10 = 10*11
%e A198455 5*6 + 6*7 = 8*9
%e A198455 5*6 + 14*15 = 15*16
%e A198455 6*7 + 9*10 = 11*12
%o A198455 (True BASIC)
%o A198455 input k
%o A198455 for a = (abs(k)-k+4)/2 to  40
%o A198455 for b = a to (a^2+abs(k)*a+2)/2
%o A198455   let t = a*(a+k)+b*(b+k)
%o A198455    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198455     if c*(c+k)=t then print a;b;c,
%o A198455 next b
%o A198455 print
%o A198455 next a
%o A198455 end
%Y A198455 Cf. A000217, A156681, A198453, A198454, A198456-A198469, A333530, A333531.
%K A198455 nonn
%O A198455 1,1
%A A198455 _Charlie Marion_, Oct 26 2011