bibkey: stephan2013a229140 authors: Ralf Stephan year: 2013 title: “OEIS A229140, Smallest k such that k^2 + l^2 = n-th number expressible as sum of two squares” doi: null url: https://oeis.org/A229140 claim: “A229140 %N: Smallest k such that k^2 + l^2 = n-th number expressible as sum of two squares (A001481). A229140 %C: Conjecture: the values between two zeros are always distinct from each other.” strata_touched:

• D5/S3/PrimeForms/StephanLeastCoordinateDistinctnessRefutation license: citation-only triage: anchor

OEIS A229140

The NAME line states:

Smallest k such that k^2 + l^2 = n-th number expressible as sum of two squares (A001481).

Ralf Stephan’s COMMENT states:

Conjecture: the values between two zeros are always distinct from each other.

The AUTHOR and OFFSET lines state:

Ralf Stephan, Sep 15 2013

1,6

Verified locator

• URL: https://oeis.org/A229140
• NAME (verbatim): Smallest k such that k^2 + l^2 = n-th number expressible as sum of two squares (A001481).
• COMMENT (verbatim): Conjecture: the values between two zeros are always distinct from each other.
• AUTHOR (verbatim): Ralf Stephan, Sep 15 2013
• OFFSET (verbatim): 1,6
• Revision history: revision #8 by Ralf Stephan at Tue Sep 17 03:55:26 EDT 2013 is the first revision carrying the word distinct; current revision #39 at Tue Sep 23 23:41:09 EDT 2025 still carries the COMMENT without a settlement.

The linked b-file already records the counterexample at lines 216 0, 218 12, 231 12, and 233 0. The values 628 and 673 therefore share the least first coordinate 12 between the consecutive zero values 625 and 676.