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

1,6

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.

Links

Table of n, a(n) for n=1..74.

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

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)).

Example

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).

Crossrefs

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

Sequence in context: A033325 A126690 A338945 * A104714 A085119 A010128

Adjacent sequences: A263004 A263005 A263006 * A263008 A263009 A263010

Keyword

nonn

Author

Wolfdieter Lang, Oct 28 2015

Status

approved