We are pleased to announce the winning sequences in the OEIS 400k celebration. Well over 100 nominations were received, covering a great many topics collectively showing that the spirit of the OEIS is alive and well.
The selection committee consisted of Sean A. Irvine, Jonas Karlsson, Hugo Pfoertner, and Neil J. A. Sloane. Committee members abstained from providing evaluations on sequences they authored or were closely involved with. The selection committee would like to thank all the people who took time to nominate a sequence.
A400000 (previously A399633) Eric Fox The city-building sequence: a(n) = the height h of the shortest building which can see exactly h earlier buildings.
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.
A399995 (previously A394611) Joshua B. Weinstein a(1) = 0. For n > 1, a(n) is the number of ways to write a(n-1) as the sum of two earlier terms with distinct positions in the sequence. A simple definition leading to a frustratingly difficult unsolved problem.
A399996 (previously A400866) Dmitry Kamenetsky Number of free polyominoes with 2n cells that can be dissected into two congruent polyominoes. The best polyomino sequence of the year.
A399997 (previously A397960) Wujie Gu a(n) is the maximum number of distinct positive differences of an n-element subset of {0, 1, ..., n*(n-1)/2}. An instant classic extremal set-theory problem.
A399998 (previously A400887) Rok Cestnik a(n+1) = a(n-a(a(n))^2) + 1, a(0) = 0. A new twist on the classic Hofstadter recurrences.
A399999 (previously A400462) Ed Pegg Jr Number of ways to cut a 30-60-90 triangle into n 30-60-90 triangles. One of several triangle dissection problems, lovely pictures.
A400001 (previously A400663) Felix Huber 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.
A400002 (previously A400976) Aidan Markey Start with a set of two adjacent points in a hexagonal lattice. At each iteration, add to the set the lattice points which are adjacent to exactly two points already in the set, but only if those two points are adjacent to each other. The sequence gives the number of points in the set after n iterations. An unusual sequence of clusters.
A400003 (previously A399179) Michael S. Branicky and N. J. A. Sloane The sequence of binary decisions that defines the unique infinite path in the base-10 comma child graph. Previously MSB/NJAS had to use Koenig's Lemma and the Axiom of Choice to show that it was possible for the kangaroo to escape death. Chris Randall and Paul Roberts showed without using AI that there is a unique path with a simple recurrence.
A400004 (previously A401021) Scott B. Farrar Half the minimum surface area of a rectangular box with positive integer side lengths and volume at least n. A new problem with a classic feel.
A400005 (previously A395645) Rémy Sigrist 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. Sequence lists squares occupied by a Red knight. A representative of many astonishing sequences of knights on an infinite chessboard, a popular topic after a Numberphile video appeared.
These are a further ten nominated sequences which the committee found particularly attractive or interesting. These sequences have all received the keyword “nice” but retain their original A-numbers.
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).
A396596 (Hal M. Switkay) Natural numbers k such that the sum of the x-th powers of the divisors of k achieves a record, for some x <= 0.
A397182 (N. J. A. Sloane) a(n) = maximum number of regions the plane can be divided into by drawing n constrained long-legged A's
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.
A399138 (Aleksei Kudriashov) a(n) = maximum number of points in an n X n X n grid with no three collinear.
A399946 (Eliott Grillet) Maximum terminal value in the Gilbreath reduction of graceful paths of order n.
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.
A401169 (Scott Duke Kominers) A quadratic form represents every Fibonacci number iff it represents these ten numbers.