Peter Kagey

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

A400615 (Jakob Süskind) Maximum number of edges in the Hasse diagram of a lattice with n elements. A400939 (Zlatko Damijanic) The halving Recaman walk: a(1) = 1; for n > 1, a(n) = a(n-1)/2 if a(n-1) is even and a(n-1)/2 has not already appeared, otherwise a(n) = a(n-1) + n.

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

A398965 (Jens Ahlström) Squares visited by a "Carpenter" (Dabbaba + Knight) moving on a spirally numbered board always to the lowest available unvisited square. A399136 (Stephen J. Pursey) a(n) is the smallest number of cells in a polycube that has a cavity consisting of exactly n cells.

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

Honorable mentions went to the following (and all received the keyword "nice") A394184 (Charles L. Hohn) Number of primitive tessellations of paths of length n in the square lattice, reduced for symmetry (with rotations, reflections, and translations not counted as distinct).

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

A400005 went to Rémy Sigrist's sequence. Consider the square spiral with its cells numbered starting at 0. Three players, Red, Green and Blue, take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of a different color. ...

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

... kangaroo to escape death. Chris Randall and Paul Roberts showed without using AI that there is a unique path with a simple recurrence."

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

... The sequence gives the number of points in the set after n iterations. "An unusual sequence of clusters."

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

A400001 went to Felix Huber's sequence. a(n) is the number of congruence classes of nondegenerate triangles whose vertices are points of an n X n X n grid. "One of several excellent Huber sequences relating to triangles."

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

A399998 went to Rok Cestnik's sequence. a(n+1) = a(n-a(a(n))^2) + 1, a(0) = 0. "A new twist on the classic Hofstadter recurrences."

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

A399996 went to Dmitry Kamenetsky's sequence. Number of free polyominoes with 2n cells that can be dissected into two congruent polyominoes. "The best polyomino sequence of the year."

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

"The height of a building in Eric Fox's City-Building sequence is determined by how many existing buildings it can see. This impressed all the judges as by far the most brilliant invention of 2026. There are already 25 other sequences that reference it."

In honor of the On-Line Encyclopedia of Integer Sequences reaching 400,000 sequences, the editors took suggestions for which sequence should be honored with the A-number A400000. The winner and the runners-up have been announced! You can see them all by following the link or reading the thread.

A sequence of squares I was doodling on graph paper in a faculty meeting: the rule is that all of the squares have integer coordinates, live in the first quadrant, are drawn in increasing order, and the "internal pattern" of any two squares must be distinct.

We draw the squares one at a time such that their lower-left corner is placed at x=0, x=1, etc. We first try to minimize the size of each square, and then minimize the (nonnegative integer) y-value. You can read about a related sequence in my Code Golf Stack Exchange question.

Check out Alexander Graham Bell’s Tetrahedral Kites from Public Domain Review! (More photos if you follow the link!) publicdomainreview.org/collection/a...

Check out Jiabao Li's project of "transforming abstract math into climbable sculptures," complete with a rendering of a mathematical playground! "What if others could literally play with math—climb on it, move around it, think about it differently?" infinitesums.simonsfoundation.org/math-ambassa...

Hey! That’s the one in the profile picture!