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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)). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..55.

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

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)).

EXAMPLE

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).

CROSSREFS

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

Sequence in context: A060234 A131270 A109223 * A283983 A016466 A293669

Adjacent sequences:  A263006 A263007 A263008 * A263010 A263011 A263012

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Oct 29 2015

STATUS

approved

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Last modified November 18 17:49 EST 2018. Contains 317323 sequences. (Running on oeis4.)