bibkey: alkan2020a335925
authors: Altug Alkan
year: 2020
title: "OEIS A335925, a(n) = a(floor((n-1)/a(n-1))) + 1 with a(1) = 1"
doi: null
url: https://oeis.org/A335925
claim: "A335925 %N: a(n) = a(floor((n-1)/a(n-1))) + 1 with a(1) = 1. A335925 %C: Least k such that a(k) = n are 1, 2, 5, 16, 65, 326, 1957, ... (Conjecture: This sequence is A000522). A335925 %A: _Altug Alkan_, Jun 30 2020"
strata_touched:
  - D5/S1/Recurrence/Invariants/SelfReferentialQuotientFirstOccurrence
license: citation-only
triage: anchor

OEIS A335925

The entry defines the sequence from index one by a(n) = a(floor((n-1)/a(n-1))) + 1, with a(1) = 1. The formal definition uses the value one at index zero only to totalize this recurrence; no source claim about index zero is asserted.

The entry records Alkan’s conjecture that the least indices carrying successive positive values form A000522. The formal threshold sequence starts with one and satisfies T(r+1) = (r+1)*T(r) + 1, so its index r corresponds to A000522(r).

Verified locator

• URL: https://oeis.org/A335925
• Locator: COMMENTS, “Least k such that a(k) = n are 1, 2, 5, 16, 65, 326, 1957, … (Conjecture: This sequence is A000522).”