%I #13 Oct 31 2015 14:34:05
%S 1,1,1,1,1,5,2,1,1,1,2,3,1,4,13,1,2,3,1,1,1,5,1,5,3,78,1,5,25,3,3,1,2,
%T 13,2,3805,4,1,1,1,36,3,1,125,5,85,4,3,1,1,41,11,53,1,12,14,732,2,569,
%U 5,1,1,1,389,13,851525,1,2,2,73,3,13,5,51
%N Second member S0(n) of the smallest positive pair (R0(n), S0(n)) for the n-th 1-happy number couple (B(n), C(n)).
%C See A263007. C(n)*a(n)^2 - B(n)*A263007(n)^2 = +1, n >= 1, with the 1-happy couple (B(n), C(n)) = (A191854(n), A191855(n)).
%C In the Zumkeller link "Initial Happy Factorization Data" given in A191860 the a(n) = S0(n) numbers appear for the t = 1 rows in column w.
%H J. H. Conway, <a href="http://www.cs.uwaterloo.ca/journals/JIS/happy.html">On Happy Factorizations</a>, J. Integer Sequences, Vol. 1, 1998, #1.
%F A191855(n)*a(n)^2 - A191854(n)*A263006(n)^2 = +1, and A263006(n) with a(n) is the smallest positive solution for the given 1-happy couple (A191854(n), A191855(n)).
%e n = 4: 1-happy number A007969(4) = 10 = 1*10 = A191854(4)*A191855(4). 10*a(4)^2 - 1*A263006(4)^2 = 10*1^2 - 1*3^2 = +1. This is the smallest positive solution for given (B, C) = (1, 10).
%Y Cf. A007969, A191854, A191855, A191860, A263006, A262025, A261250.
%K nonn
%O 1,6
%A _Wolfdieter Lang_, Oct 28 2015