bibkey: yanev2016a090079
authors: Reinhard Zumkeller; Velin Yanev
year: 2016
title: "OEIS A090079, binary run compression"
doi: null
url: https://oeis.org/A090079
claim: "In binary expansion of n: reduce contiguous blocks of 0's to 0 and contiguous blocks of 1's to 1. Conjecture: a(n) = (2^(A005811(n)+1) + (1-(-1)^n)/2 - 2)/3. - _Velin Yanev_, Dec 12 2016"
strata_touched:
  - D5/S1/Digit/YanevRunCompressionClosedForm
license: citation-only
triage: anchor

OEIS A090079, binary run compression

The entry defines binary run compression. Yanev’s formula expresses its value using the number of binary runs, A005811(n), and the parity of n. The integer identity (1-(-1)^n)/2 = n mod 2 supplies the parity indicator. The Lean statement is multiplied by 3 to stay in ℕ, with truncated natural subtraction, and includes zero via its empty binary digit list.

Verified locator

• URL: https://oeis.org/A090079
• %N (verbatim): In binary expansion of n: reduce contiguous blocks of 0’s to 0 and contiguous blocks of 1’s to 1.
• %F (verbatim): Conjecture: a(n) = (2^(A005811(n)+1) + (1-(-1)^n)/2 - 2)/3. - Velin Yanev, Dec 12 2016
• %A (verbatim): Reinhard Zumkeller, Nov 20 2003

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