A263009 - OEIS

%I #6 Oct 31 2015 14:35:39

%S 1,3,1,1,1,3,5,1,1,39,3,1,1,9,7,1,1,3,1,27,59,3,9,1,1,1,3,15,5,1,477,

%T 1,3,7,11,1,1,2175,17,9,7,3,747,1,41571,1,5,19,627,13,1,1,9,5,153

%N Second member U0(n) of the smallest positive pair (T0(n), U0(n)) for the n-th 2-happy number couple (D(n), E(n)).

%C See A263008. E(n)*a(n)^2 - D(n)*A263008(n)^2 = +2, n >= 1, with the 2-happy couple (D(n), E(n)) = (A191856(n), A191857(n)). The 2-happy numbers D(n)*E(n) are given by A007970(n).

%C In the Zumkeller link "Initial Happy Factorization Data" given in A191860 the a(n) = U0(n) numbers appear for the t = 2 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 A191857(n)*a(n)^2 - A191856(n)*A263008(n)^2  = +2, and A263008(n) with a(n) is the smallest positive

%F solution for the given 1-happy couple (A191856(n), A191857(n)).

%e n = 4: 2-happy number A007970(4) = 11 = 1*11 =

%e   A191856(4)*A191857(4). 11*a(4)^2 - 1*A263008(4)^2 = 11*1^2 - 1*3^2 = +2. This is the smallest positive solution for given (D, E) = (1, 11).

%Y Cf. A007970, A191856, A191857, A191860, A263008, A262026 , A262027, A262028.

%K nonn

%O 1,2

%A _Wolfdieter Lang_, Oct 29 2015