bibkey: oeis2026a115803
authors: OEIS Foundation
year: 2026
title: "OEIS A115803 and A115805: carryless multiplier containment"
doi: null
url: https://oeis.org/A115803
claim: "A115805 records the condition 13*k = A048720(29,k), while A115803 records 11*k = A048720(31,k); the qualified target is containment of the former solution set in the latter. A048720 is binary polynomial multiplication over GF(2)."
strata_touched:
  - D5/S1/Digit/Admissibility/CarrylessThirteenElevenContainment
license: CC-BY-SA-4.0
triage: anchor

Carryless multiplier containment

The source sequences use ordinary multiplication on the left and the binary polynomial multiplication table A048720 on the right. The target assertion is the all-natural-number implication

$$13k=C(29,k)⟹11k=C(31,k).$$

The retained source scope is the OEIS internal pages for A115803, A115805 and A048720. It records source definitions and conjectured containment only; the finite checks reported there are not universal proofs. This note does not make a worldwide-priority or exhaustive-literature claim.

The source correspondence uses A115805 revision 14, including its containment cross-reference, A115803 revision 13, and A048720 revision 62. Antti Karttunen authored the two multiplier sequences in 2006 and the carryless operation entry in 1999. The OEIS Foundation citation year 2026 identifies the institutional database citation, rather than the original publication of the question. The source license is CC-BY-SA-4.0. This note’s use is citation only; that usage description is not a license.

Verified locator

• https://oeis.org/A115805/internal : NAME gives 13*k=A048720(29,k) and CROSSREFS records the containment conjecture.
• https://oeis.org/A115803/internal : NAME gives 11*k=A048720(31,k).
• https://oeis.org/A048720/internal : the square-form program multiplies binary coefficient polynomials modulo two.