OFFSET
1,2
COMMENTS
The 1-happy numbers B(n)*C(n) are given in A007969(n) (called rectangular numbers in the Conway paper). B(n) = A191854(n), C(n) = A191855(n). Here the corresponding smallest positive numbers satisfying C(n)*S0(n)^2 - B(n)*R0(n)^2 = +1, n >= 1, are given as R0(n) = a(n) and S0(n) = A263007(n).
For a proof of Conway's happy number factorization theorem see the W. Lang link under A007970.
In the W. Lang link given in A007969 the first C(n), B(n), S0(n), R0(n) numbers are given in the Table for d(n) = A007969(n), n >= 1.
In the Zumkeller link "Initial Happy Factorization Data" given in A191860 the a(n) = R0(n) numbers appear for the t = 1 rows in column v.
LINKS
J. H. Conway, On Happy Factorizations, J. Integer Sequences, Vol. 1, 1998, #1.
FORMULA
EXAMPLE
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Oct 28 2015
STATUS
approved