reviewed

approved

proposed

reviewed

editing

proposed

Note that in base b = 2, no values of x satisying satisfying (*) exist, and the theorem asserts that D(2) is empty. In fact it is easy to check directly that every commas sequence in base 2 is infinite. If the initial term is 0 or 1 mod 4 then the sequence will merge with A042948, and if the initial term is 2 or 3 mod 4 then the sequence will merge with A042964.

approved

editing

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, <a href="http://arxiv.org/abs/2401.14346">arXiv:2401.14346</a>, <a href="https://vimeowww.youtube.com/906608376watch?sharev=copy_EHAdf6izPI">VimeoYoutube</a>

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, <a href="http://neilsloane.com/doc/Commas1.pdf">The Comma Sequence: A Simple Sequence With Bizarre Properties, <a href="http://arxiv.org/abs/2401.14346">arXiv:2401.14346</a>, <a href="https://vimeo.com/906608376?share=copy">Vimeo</a>, Draft, 22 Jan 2024

editing

approved

Éric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, Manuscript in preparation, Dec., 2023.

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, <a href="http://neilsloane.com/A367341doc/a367341_1Commas1.txtpdf">The comma-successor theoremComma Sequence: A Simple Sequence With Bizarre Properties</a>., Draft, 22 Jan 2024

approved

editing

editing

approved

Note that in base b = 2, no values of x satisying (*) exist, and the theorem asserts that D(2) is empty. In fact it is easy to check directly that every commas sequence in base 2 is infinite. If the initial term is 0 or 1 (mod 4) then the sequence will merge with A042948; otherwise , and if the initial term is 2 or 3 mod 4 then the sequence will merge with A042964.

Éric Angelini, Michael S. Branicky, Giovanni Resta, and N. J. A. Sloane, and David W. Wilson, The Commas Comma Sequence: A Simple Sequence With Bizarre Properties, Manuscript in preparation, Dec., 2023.

approved

editing