# [seqfan] Re: proposals

Neil Sloane njasloane at gmail.com
Sat Nov 24 06:10:00 CET 2018

```John,  sure, go ahead and submit them!  Thanks.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

On Fri, Nov 23, 2018 at 3:19 PM Mason John <john.mason at lispa.it> wrote:

> Dear Seqfans
> I will publish these sequences if they are considered interesting.
>
> 1. a(n) = number of occurrences of the decimal representation of n  in the
> concatenation of all terms preceding a(n), or n there are no such
> occurrences. Clarification: define the number of occurrences of string s in
> string t to be the number of positions within t that have a perfect match
> with the digits in s. Thus the number of occurrences of 11 in 1111 is 3 and
> not 2.
>
> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 14, 15, 16, 17, 18, 19, 20, 21,
> 22, 1, 24, 25, 26, 27, 28, 29, 30, 1, 32, 33, 1, 35, 36, 37, 38, 39, 40, 1,
> 1, 43, 44, 1, 46, 47, 48, 49, 50, 1, 1, 1, 54, 55, 1, 57, 58, 59, 60, 1, 1,
> 1, 1, 65, 66, 1, 68, 69, 70, 1, 1, 1, 1, 1, 76, 77, 1, 79, 80, 1, 1, 1, 1,
> 1, 1, 87, 88, 1, 90, 1, 1, 1, 1, 1, 1, 1, 1, 99, 100, 1, 102, 103, 104,
> 105, 106, 107, 108, 109, 1, 18
>
> 2. Lexicographically least infinite sequence of positive integers such
> that no term, in its decimal representation, is a substring of any other
> term of the sequence.
>
> 1, 2, 3, 4, 5, 6, 7, 8, 99, 909, 9009, 900009, 9000009<tel:9000009>,
> 90000009<tel:90000009>, 900000009<tel:900000009>
>
> 3. Lexicographically least infinite sequence of positive integers such
> that no term, in its decimal representation, has more than one occurrence
> in the string formed by the concatenation all the terms of the sequence.
>
> 1, 2, 3, 4, 5, 6, 7, 8, 909, 9009, 900009, 9000009<tel:9000009>,
> 90000009<tel:90000009>, 900000009<tel:900000009>
>
> John
>
>
>
>
>
> --
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>

```