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 A137453 a(0) = 2, a(1) = 9; thereafter, a(n) = a(n-1)*a(n-2) mod (a(n-1)+a(n-2)). 1
 2, 9, 7, 15, 17, 31, 47, 53, 91, 71, 143, 95, 19, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Playing around with different starting pairs, it looks like all starting pairs either end in a loop, or by going to the pair (0,0) which is either a loop or a singularity, depending on whether you take 0 mod 0 as being 0 or undefined. Furthermore, you can go an arbitrarily long time without looping. Take for large a: .., 6*a+6, 6*a, ... The next term is 6*a-6, and progressively it goes down the ladder by steps of 6 until it terminates at ..., 18, 12, 6, 0, 0. In a few minutes of searching, the longest sequence I could find which eventually loops without going to zero was the sequence starting with (29,574), which hits 855 at the 79th term and then stays at 855. - Jack Brennan LINKS Eric Angelini, ModuloPlay E. Angelini, ModuloPlay [Cached, with permission] EXAMPLE 2*9 mod 2+9 = 18 mod 11 = 7. CROSSREFS Sequence in context: A160439 A245287 A254595 * A063381 A019078 A205384 Adjacent sequences:  A137450 A137451 A137452 * A137454 A137455 A137456 KEYWORD nonn AUTHOR Eric Angelini, Jul 07 2008 EXTENSIONS More terms from Jack Brennen, Jul 07 2008 STATUS approved

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Last modified July 15 20:00 EDT 2019. Contains 325056 sequences. (Running on oeis4.)