Metadata
bibkey: zumkeller2004a097602
authors: Reinhard Zumkeller; Vladeta Jovovic
year: 2004
title: "OEIS A097602, a(n+1) = a(n) + number of squares so far; a(1) = 1"
doi: null
url: https://oeis.org/A097602
claim: "A097602 %N: a(n+1) = a(n) + number of squares so far; a(1) = 1. A097602 %C: Conjecture: a(n) = m^2 iff m mod 3 > 0. A097602 %C: a(n) is a square iff n is congruent to {1, 4} mod 9. - _Vladeta Jovovic_, Aug 30 2004 A097602 %F: a(9*n+1) = (3*n+1)^2; a(9*n+4) = (3*n+2)^2. A097602 %A: _Reinhard Zumkeller_, Aug 30 2004"
strata_touched:
- D5/S1/Recurrence/Invariants/SquareCountingRecurrenceSquarePositions
license: citation-only
triage: anchor
OEIS A097602
The entry defines a sequence beginning at index one by adding the number of square values already seen. The formal definition uses zero at index zero only to totalize the recurrence; no source claim about index zero is asserted.
The entry records Zumkeller’s conjecture that the square values attained by the sequence have roots not divisible by three. It also records Jovovic’s assertion that square terms occur exactly at indices congruent to one or four modulo nine.
Verified locator
- URL: https://oeis.org/A097602
- Locator: COMMENTS, “Conjecture: a(n) = m^2 iff m mod 3 > 0.”