Metadata
bibkey: zumkeller2007a131853
authors: Reinhard Zumkeller
year: 2007
title: "OEIS A131853, Numbers m such that z(m)=(0,0) with z as defined in A131851"
doi: null
url: https://oeis.org/A131853
claim: "A131853 %N: Numbers m such that z(m)=(0,0) with z as defined in A131851. A131853 %C: Intersection of A131854 and A131855: A131851(a(n))=0, A131852(a(n))=0; A131853 %C: conjecture: a(n) mod 5 = 0. A131853 %A: _Reinhard Zumkeller_, Jul 22 2007 A131851 %N: Real part of the function z(n)=Sum(d(k)*i^k: d as in n=Sum(d(k)*2^k), i=sqrt(-1)). A131851 %F: z(n) = if n=0 then (0, 0) else z(floor(n/2))*(0, 1) + (n mod 2, 0), complex multiplication."
strata_touched:
- D5/S1/Digit/ZumkellerBinaryGaussianEvaluationZeroMultipleOfFive
license: citation-only
triage: anchor
OEIS A131853
The entry lists the arguments whose binary digit polynomial vanishes at the Gaussian imaginary unit and records Zumkeller’s divisibility conjecture.
Verified locator
- URL: https://oeis.org/A131853
- Locator: COMMENTS, “conjecture: a(n) mod 5 = 0.”
- Reduction: Modulo 5 the proof reduces i to 2, since 2² = 4 ≡ −1, and obtains m ≡ Re z(m) + 2·Im z(m) (mod 5); this reduction is elementary and carries no priority claim.