cp's OEIS Frontend

a(n) is the smallest positive integer such that A160371(a(n)) > n.

Chess diagrams are chess positions without regard to whether castling or en passant capturing is possible. The condition that the diagram cannot be obtained in fewer than n plies means that each legal chess diagram is counted exactly once in this sequence, indexed by the length of the shortest game(s) to reach it. Therefore, this sequence is finite and its sum equals the number of legal chess diagrams, estimated to be between 10^43 and 10^47.

Chess diagrams are chess positions without regard to whether castling or en passant capturing is possible. They are counted in A019319. A shortest proof game (SPG) is a classic type of chess problem. Most published SPGs are dual-free (have only one solution), which is why we count diagrams that are obtained in exactly one way in the minimum number of plies.

Among all the proof game problems counted in A090051, this is the number of problems ending in checkmate.

Among all the proof game problems counted in A090051, this is the number of problems where all the surviving pieces are apparently on their start squares.

Definition: position = position with castling and en passant information, diagram = position without castling and en passant information.

The positions are taken from the sets that are counted in A083276.

Chess diagrams are chess positions without regard to whether castling or en passant capturing is possible. They are counted in A019319. A proof game is a classic type of chess problem.