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.
a(2)=6: (i) Generate 1 by burning one rope from one end. (ii) Generate 2 by burning one rope from one end at t=0 and the other afterwards at t=1 from one end. (iii) Generate 1/2 by burning 1 rope from both ends. (iv) Generate 3/2 by burning 1 rope from one end at t=0 then the other from both ends at t=1 (or swapped order). (v) Generate 3/4 by burning one rope at t=0 from both ends, starting the other also at t=0 at one end, and lighting the other's second end at t=1/2 when the first rope's flames have met, so the 2nd rope's flames finish at t=3/4. (vi) Generate 1/4 using the technique for 3/4 and measuring the time between t=1/2 and t=3/4. For n = 3 the a(3) = 15 solutions are 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1, 9/8, 5/4, 3/2, 7/4, 2, 5/2, 3.
a(1) = 2 because S(1) = {0, 1/2};
a(2) = 4 because S(2) = {0, 1/2, 3/4, 1};
a(3) = 9 because S(3) = {0, 1/2, 3/4, 7/8, 1, 9/8, 5/4, 11/8, 3/2}.
s:= proc(n) option remember; `if`(n=0, {0}, (l-> (m-> {seq([2*x, seq(
`if`(abs(x-y) nops(s(n)):
seq(a(n), n=0..10); # Alois P. Heinz, Apr 09 2021
S[n_]:=S[n]=If[n==0,{0},S[n-1]\[Union]Map[(#[[1]]+#[[2]]+1)/2&,Select[Tuples[S[n-1],{2}],Abs[#[[1]]-#[[2]]]<1&]]]; Table[Length[S[n]],{n,0,12}]
\\ See Corneth link. David A. Corneth, Apr 09 2021
Comments