A263007 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)).

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, 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, 5, 1, 1, 1, 389, 13, 851525, 1, 2, 2, 73, 3, 13, 5, 51

Offset: 1

Author

Wolfdieter Lang, Oct 28 2015

Keywords

• nonn

Comments

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)).

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.

Examples

			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).
		

Links

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

Crossrefs

Cf. A007969, A191854, A191855, A191860, A263006, A262025, A261250.

Formula

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)).