A263009 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)).

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

Offset: 1

Author

Wolfdieter Lang, Oct 29 2015

Keywords

• nonn

Comments

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).

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.

Examples

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

Links

• J. H. Conway, On Happy Factorizations, J. Integer Sequences, Vol. 1, 1998, #1.

Crossrefs

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

Formula

A191857(n)*a(n)^2 - A191856(n)*A263008(n)^2 = +2, and A263008(n) with a(n) is the smallest positive

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