4 May
2016
4 May
'16
9:37 p.m.
Must every sequence of squarefree positive integers satisfying the recurrence f(n) = SquarefreePart(f(n-1)+f(n-2)) eventually enter the cycle 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, ...? E.g., 7, 4, 11, 15, 26, 41, 67, 3, 70, 73, 143, 6, 149, 155, 19, 174, 193, 367, 35, 402, 437, 839, 319, 1158, 1477, 2635, 257, 723, 5, 182, 187, 41, 57, 2, 59, 61, 30, 91, 1, 23, 6, 29, 35, 1, 1, 2, 3, 5, 2, 7, ... (This probably isn't new, but you never know.) Jim