bibkey: cloitre2002a076502 authors: Benoit Cloitre year: 2002 title: “OEIS A076502, a(1)=1, a(n)=n-a(n-a(n-a(n-1)))” doi: null url: https://oeis.org/A076502 claim: “a(1)=1, a(n)=n-a(n-a(n-a(n-1))); Conjecture : a(n) - cn is bounded and a(n)=floor(cn) + 0 + 1 or +2 - Benoit Cloitre, Nov 08 2002; a(n) is asymptotic to cn with c=0.5698..is the positive root of x^3-x^2+2x-1 - Benoit Cloitre, Nov 08 2002” strata_touched:

• D5/S1/Recurrence/Invariants/CloitreNestedRecurrenceFloorRefutation license: citation-only triage: anchor

OEIS A076502

The NAME line defines the nested recurrence:

a(1)=1, a(n)=n-a(n-a(n-a(n-1)))

The 2002 comment states a conjunction of bounded error and three allowed floor offsets. The theorem cited by this note refutes the floor-offset conjunct at n = 1167. It makes no assertion about boundedness or asymptotic growth.

Verified locator

• URL: https://oeis.org/A076502
• NAME (verbatim): a(1)=1, a(n)=n-a(n-a(n-a(n-1)))
• COMMENTS conjecture line (verbatim): Conjecture : a(n) - cn is bounded and a(n)=floor(cn) + 0 + 1 or +2 - Benoit Cloitre, Nov 08 2002
• FORMULA (verbatim): a(n) is asymptotic to cn with c=0.5698..is the positive root of x^3-x^2+2x-1 - Benoit Cloitre, Nov 08 2002