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bibkey: marcus2021a344083 authors: Michel Marcus year: 2021 title: “OEIS A344083, a(n) = f(x)+f(y)+f(z), where (x,y,h) is the n-th Pythagorean triple listed in (A046083, A046084, A009000), and f(m)=A176775(m) is the index of m as k-gonal number for the smallest possible k” doi: null url: https://oeis.org/A344083 claim: “A090467 consists of numbers not of the form 1 + km(m-1)/2 - (m-1)^2 for k > 2 and m > 2. A344083 %C, May 09 2021: Conjecture: there are no other Pythagorean triples that give this minimum. In other words, it is the only triple with 3 A090467 terms. - Michel Marcus” strata_touched:

  • D5/S3/Arith/Congruence/MarcusPythagoreanNonpolygonalTriple license: citation-only triage: anchor

OEIS A344083 and A090467

The A344083 NAME states:

a(n) = f(x)+f(y)+f(z), where (x,y,h) is the n-th Pythagorean triple listed in (A046083, A046084, A009000), and f(m)=A176775(m) is the index of m as k-gonal number for the smallest possible k.

The A090467 NAME states:

Numbers which are not regular figurative or polygonal numbers of order greater than 2. That is, numbers not of the form 1 + km(m-1)/2 - (m-1)^2 where k > 2 and m > 2.

Michel Marcus’s A344083 COMMENT of May 9, 2021 states:

Conjecture: there are no other Pythagorean triples that give this minimum. In other words, it is the only triple with 3 A090467 terms. - Michel Marcus, May 09 2021

The formal definition uses the equal subtraction-free natural-number expression m + (k - 2) * Nat.choose m 2. For k > 2 and m > 2, this equals the printed A090467 expression, with / interpreted as natural-number division.

Verified locator

  • A344083: https://oeis.org/A344083
  • A090467: https://oeis.org/A090467
  • A344083 NAME (verbatim): a(n) = f(x)+f(y)+f(z), where (x,y,h) is the n-th Pythagorean triple listed in (A046083, A046084, A009000), and f(m)=A176775(m) is the index of m as k-gonal number for the smallest possible k.
  • A090467 NAME (verbatim): Numbers which are not regular figurative or polygonal numbers of order greater than 2. That is, numbers not of the form 1 + km(m-1)/2 - (m-1)^2 where k > 2 and m > 2.
  • A344083 COMMENT, May 09 2021 (verbatim): Conjecture: there are no other Pythagorean triples that give this minimum. In other words, it is the only triple with 3 A090467 terms. - Michel Marcus, May 09 2021