PK's OEIS sequences in Haskell
In November 2016, I composed a short list of my favorite original sequences:
- A277781: a(n) is the least k > n such that n*k or n*k^2 is a cube.
- A277494: a(n) = smallest m for which there is a sequence n = b_1 < b_2 ≤ b_3 ≤ ... ≤ b_t = m such that b_1*b_2*...*b_t is a perfect cube.
- A276164: a(n) is the maximum first-player score of a "Coins in a Row" game over all permutations of coins 1..n with both players using a minimax strategy.
- A275815: Maximum total number of possible moves that any number of queens of the same color can make on an n X n chessboard.
- A275288: Least k such that there exists a sequence b_1 < b_2 < ... < b_t = k that includes n and has a reciprocal sum of 1.
- A272573: Start a spiral of numbers on a hexagonal tiling, with the initial hexagon as a(1) = 1. a(n) is the smallest positive integer not equal to or previously adjacent to its neighbors.
- A272020: Irregular triangle read by rows: strictly decreasing sequences of positive numbers given in lexicographic order.
- A269045: Indices k such that A006255(k) != A070229(k); that is, the kth term of Ron Graham's sequence is not equal to k + lpf(k).
- A261865: a(n) is the least integer k such that some multiple of sqrt(k) falls strictly between n and n+1.
- A260643: Start a spiral of numbers on a square grid, with the initial square as a(1) = 1. a(n) is the smallest positive integer not equal to or previously adjacent (horizontally/vertically) to its neighbors. (See the Comments section for a more exact definition.)
- A259527: a(n) counts the number of sequences n = b_1 < b_2 < ... < b_t = A006255(n) such that b_1*b_2*...*b_t is a perfect square.
- A259280: a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings of length greater than 1.
- A255167: a(n) = A072905(n) - A006255(n). (The gap between A006255(n) and its naïve upper bound.)
- A254128: Number of binary strings of length n that begin with an odd-length palindrome.
- A248663: a(1) = 0; a(A000040(n)) = 2^(n-1), and a(n*m) = a(n) XOR a(m).
- A248122: Number of strings of length n over a three-letter alphabet that begin with a nontrivial palindrome.
Two original sequences with the keyword "look"
Start a spiral of numbers on a square grid, with the initial square as a(1) = 1. a(n) is the smallest positive integer not equal to or previously adjacent (horizontally/vertically) to its neighbors.
Product of all parts in Zeckendorf representation of n.