bibkey: quet2003a079278 authors: Leroy Quet; N. J. A. Sloane year: 2003 title: “OEIS A079278, denominators of the rational iteration b(n) = b(n-1) + 1/(1 + 1/b(n-1))” doi: null url: https://oeis.org/A079278 claim: “%N A079278 Define a rational sequence {b(n)} as b(1) = 1, b(n) = b(n-1) + 1/(1 + 1/b(n-1)) for n > 1; a(n) is the denominator of b(n). %F A079278 Conjecture (Quet): a(m+1) = a(m)^2 + a(m)^3 / a(m-1)^2 - a(m)*a(m-1)^2 for m >= 2.” strata_touched:

• D5/S1/Recurrence/Residue/QuetRationalIterationDenominator license: citation-only triage: anchor

OEIS A079278

The NAME line defines a rational iteration and takes the reduced denominator of each rational value. The FORMULA line records Leroy Quet’s conjectured recurrence for those denominators.

Verified locator

• URL: https://oeis.org/A079278
• NAME (%N, verbatim): Define a rational sequence {b(n)} as b(1) = 1, b(n) = b(n-1) + 1/(1 + 1/b(n-1)) for n > 1; a(n) is the denominator of b(n).
• FORMULA (%F, verbatim): Conjecture (Quet): a(m+1) = a(m)^2 + a(m)^3 / a(m-1)^2 - a(m)*a(m-1)^2 for m >= 2.
• DATE (%D, verbatim): Suggested by Leroy Quet, Feb 14 2003.
• AUTHOR (%A, verbatim): N. J. A. Sloane, Feb 16 2003
• OFFSET (%O, verbatim): 1,2

Revision #45 (Jul 12 2022 20:55:10) still carries Conjecture (Quet) in the FORMULA line, without a settlement comment or proof link.