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 A249973 Positive integers A when the positive roots of r^2 = Ar + B are listed in increasing order. 1
 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 1, 2, 3, 4, 1, 2, 3, 1, 4, 2, 1, 3, 2, 4, 1, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 5, 3, 1, 4, 2, 1, 3, 5, 2, 4, 1, 3, 2, 5, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Generalize the Fibonacci sequence recurrence equation as: F_(n+1) = A*F_n + B*F_(n-1), where A and B are positive integers. As n goes to infinity, the ratio F_n / F_(n-1) approaches the positive real number r = (A + sqrt(A*A + 4B))/2. This sequence gives the A values in increasing order of r. In case of a tie in r values, then sort in increasing order of sqrt(A*A + B*B). This A sequence appears to be the ordinal transform of the B sequence (A249974) and vice versa. The associative arrays of A and B are transposes. The first row of A's associative array seems to be A006000. For the A and B values leading to a positive integer limit r see a comment in A063929. - Wolfdieter Lang, Jan 12 2015 LINKS Table of n, a(n) for n=1..78. EXAMPLE a(6) = 2 because the 6th smallest value of r (approximately 2.732050808) is that for A=2, B=2. PROG (PARI) \\ see A249974 CROSSREFS Cf. A249974, A006000. Sequence in context: A341765 A104248 A358359 * A343854 A069349 A167404 Adjacent sequences: A249970 A249971 A249972 * A249974 A249975 A249976 KEYWORD easy,nonn AUTHOR Kerry Mitchell, Nov 09 2014 EXTENSIONS Edited. - Wolfdieter Lang, Jan 11 2015 STATUS approved

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Last modified June 13 05:35 EDT 2024. Contains 373366 sequences. (Running on oeis4.)