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 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)). 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A113103 A033325 A126690 * A104714 A085119 A010128 Adjacent sequences:  A263004 A263005 A263006 * A263008 A263009 A263010 KEYWORD nonn AUTHOR Wolfdieter Lang, Oct 28 2015 STATUS approved

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Last modified October 16 20:34 EDT 2018. Contains 316275 sequences. (Running on oeis4.)