This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A304120 #40 Jun 18 2019 10:00:44 %S A304120 2,15,305,6479 %N A304120 a(n) is the least k such that there is a permutation of the positive integers from 1 through k for which every pair of adjacent terms sums to a perfect power with exponent n. %C A304120 From _Jordan D Fredette_, May 28 2019: (Start) %C A304120 I was helped immensely by my friend Christian Burns who is an expert programmer. %C A304120 I also worked with my friend Josiah Findley. Without him I likely would have never figured this out. %C A304120 Essentially, I discovered that when arranging the numbers 1..k so that any two next to each other add up to a perfect power, we need not check every single permutation. %C A304120 In fact, the best method is to list all the different ways to add up two numbers to get each of the powers which are greater than 1 but less than 2k. %C A304120 If any number shows up only once in this list, then it must be an endpoint. %C A304120 Once the endpoints are determined, any number that only shows up twice must be connected to the two other numbers with which it is paired in the list. %C A304120 This will result in strings of numbers which must be a part of the permutation. %C A304120 If the same number is at the end of two different strings then those strings must be joined. %C A304120 Thus, the number of permutations to be checked is further decreased. %C A304120 Basically, Christian was able to implement this as a program and found that 6479 is the smallest k for which the numbers 1..k can be arranged so that any two next to each other add up to a perfect fourth power. (End) %H A304120 Moritz Firsching, <a href="https://mathoverflow.net/q/199846">Arranging numbers from 1 to n such that the sum of every two adjacent numbers is a perfect power</a>, MathOverflow. %H A304120 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_311.htm">Puzzle 311: Sum to a cube</a> %e A304120 a(1) = 2 as the permutation (1, 2) of the integers has the property that the adjacent terms sum to a power of 1. %e A304120 a(2) = 15 as the permutation of the positive integers 1 through 15 [8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9] has the property that every pair of adjacent terms sums to a power with exponent n = 2 (a square). %o A304120 (Sage) See MathOverflow link. %Y A304120 For n=2, see A090461. %K A304120 nonn,bref,more %O A304120 1,1 %A A304120 _Benjamin Knight_, May 06 2018 %E A304120 a(4) from _Jordan D Fredette_, May 28 2019