bibkey: orlovsky2009a165719 authors: Vladimir Joseph Stephan Orlovsky; Bill McEachen year: 2009 title: “OEIS A165719, Integers of the form k*(k+9)/8” doi: null url: https://oeis.org/A165719 claim: “%C A165719 Only one term is a prime number (17). Are all others composite? %F A165719 Conjecture: Valid k values are pairs of the form (8m-1,8m) for m=1,2,3…. If true, 17 is the only prime term. - Bill McEachen, May 06 2026” strata_touched:

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

OEIS A165719

The entry asks whether every integral value other than 17 is composite and conjectures that the positive parameters are the pairs immediately before and at positive multiples of eight.

Verified locator

• URL: https://oeis.org/A165719
• NAME (verbatim): %N A165719 Integers of the form k*(k+9)/8.
• COMMENT (verbatim): %C A165719 Only one term is a prime number (17). Are all others composite?
• FORMULA (verbatim): %F A165719 Conjecture: Valid k values are pairs of the form (8m-1,8m) for m=1,2,3…. If true, 17 is the only prime term. - Bill McEachen, May 06 2026
• AUTHOR (verbatim): %A A165719 Vladimir Joseph Stephan Orlovsky, Sep 24 2009
• OFFSET (verbatim): %O A165719 1,1

Revision #24 (May 14 2026 00:56:29) contains both assertions without a settlement comment or proof link. Its example explicitly takes k=1,2,… and retains only integral values. The sole link is the OEIS internal linear-recurrence index; there is no bibliographic entry. The prime-term question occurs in archived revision #1 (June 1 2010); McEachen’s parameter conjecture was added in revisions #18/#19 (May 6 2026).