Top chap (and newest Aperiodipal?) Neil Sloane, founder of the Online Encyclopedia of Integer Sequences, wrote in to direct our attention towards a “best new integer sequence” contest being run on the sequence-fans mailing list.

Any sequence submitted between the middle of December and the middle of January is eligible. The winners (of which there will be at least three) will each receive a signed copy of the original 1973 Handbook of Integer Sequences, as well as the highly coveted “nice” keyword on their encyclopedia entries.

Because this is the OEIS, the method for keeping track of entries is quite obtuse: sequences entered in the competition have the word CONTEST added to the start of their comments section through a draft edit, and you can find all sequences in the contest by trawling through the OEIS’s draft edits list. Because I love you, I’ve been through the list and compiled this list of current entries.

*(Scroll to the bottom of each sequence’s page to see the entry as it stands after the proposed edits.)*

- A234285 – Positive odd numbers $n$ such that $\sigma(m)-2m$ is never equal to $n$, where $\sigma(\cdot)$ is the sum of divisors function A000203. Conjectural. (N.J.A. Sloane)
- A233940 – Number $T(n,k)$ of binary words of length $n$ with exactly $k$ (possibly overlapping) occurrences of the subword given by the binary expansion of $n$; triangle $T(n,k)$, $n \geq 0$, read by rows. (Alois P. Heinz)
- A233332 – Irregular array read by rows: $A(n,k)$ = number of first coronas of a fixed rhombus $r_{n,k}$ in the plane, $n \geq 2$, $1 \leq k \leq \left \lfloor \frac{n}{2} \right \rfloor$. (L. Edson Jeffery)
- A234537 – Number of partitions of $2n$ into two odd parts with at least 1 composite part less than $2n-1$. (Wesley Ivan Hurt)
- A233564 – Positive integers which in binary are concatenation of distinct parts of the form $10 \dots 0$ with nonnegative number of zeros. (Vladimir Shevelev)
- A233700 – Decimal expansion of $1/\sin(\arctan(1/\tau))$ or $\tau/\sin(\arctan(\tau))$ where $\tau = 2\pi$: hypotenuse for a right triangle of equal area to a disk. (John W. Nicholson)
- A234367 – Numbers such that $\operatorname{gcd}(\sigma(n), n) \neq 1$ and still have $\operatorname{numerator}\left( \frac{\sigma(n)}{n} \right) \gt n$. (Michel Marcus)
- A234566 – $\frac{1}{a(n)}$ is the area of the smallest triangle delimited by 3 lines each passing through at least 2 points of a $n \times n$ unitary spaced grid. (Giovanni Resta)
- A234434 – Number of shapes of grid-filling curves (on the triangular grid) with turns by $0$, $+120$, or $-120$ degrees that are generated by Lindenmayer-systems with just one symbol apart from the turns. (Joerg Arndt)
- A234840 – Self-inverse and multiplicative permutation of integers. (Antti Karttunen)
- A234092 – Limit of $v(m,n)$ as $m \to \infty$, where $v(m,n)$ is the number of distinct terms in the $n$
^{th}partition of $m$ in Mathematica (lexicographic) ordering of the partitions of $m$. (Clark Kimberling) - A234586 – Odd-indexed terms are absolute values of differences. (Eric Angelini)
- A235062 – Odd part of $n$
^{th}superfactorial (A000178). (Ralf Stephan) - A234968 – Totally symmetric partitions of $n$ of any dimension. (Graham H. Hawkes)
- A234642 – Smallest $x$ such that $x \bmod \phi(x) = n$, or $0$ if no such $x$ exists. (Charles R Greathouse IV)
- A234013 – Number of maximally biased free polyominoes with $n$ squares. (John Mason)
- A231345 – Triangle read by rows: $T(n,k)$, $n \geq 1$, $k \geq 1$, in which column $k$ lists the odd numbers interleaved with $k-1$ zeros but $T(n,1) = -1$ and the first element of column $k$ is in row $\frac{k(k+1)}{2}$. (Omer E. Pol)
- A229037 – Sequence of positive integers where each is chosen to be as small as possible subject to the condition that no three terms $a(j)$, $a(j+k)$, $a(j+2k)$ (for any $j$ and $k$) form an arithmetic progression. (Jack Grahl)
- A234472 – Numbers which when raised to the fourth power and written backwards give a square. (Colin Barker)
- A234849 – Positions of records in iterated MD5 applied to empty string. (Sean A. Irvine)
- A234932 – The product $a(n) \times a(n+1)$ can be written using the digits of $\{a(n),a(n+1)\}$; always choose the smallest possible unused positive integer. (Claudio Meller)
- A233466 – Numbers $n$ such that $\phi(n) = \frac{n-5}{2}$. (Farideh Firoozbakht)

There are certainly some corkers in there! Entries must be submitted before January the 11th, and the winners will be announced on the 18th.

### More information

OEIS contest for January AMS/MAA meeting – post by Tony Noe on the SeqFan mailing list.

OEIS Drafts in Progress (where submitted sequences live).