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COMMENT
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Sequence repeats cyclically. Conjecture: sequence ends with cycle for any positive a(1) and a(2). This has been checked for a(1)=1 and a(2)=1,...,2000. Some other cases shown below: a(1), a(2), length of s, sequence s 1,1,10,{1,1,2,3,5,4,3,7,2,3}, 1,2,9,{1,2,3,5,4,3,7,2,3}, 1,3,9,{1,3,2,5,7,4,11,3,2}, 1,4,20,{1,4,5,3,4,7,11,6,17,23,8,31,3,2,5,7,4,11,3,2}, 1,5,12,{1,5,2,7,3,2,5,7,4,11,3,2}, 1,6,23,{1,6,7,13,4,17,3,4,7,11,6,17,23,8,31,3,2,5,7,4,11,3,2}, 1,7,9,{1,7,4,11,3,2,5,7,4}, 1,8,30,{1,8,3,11,2,13,3,8,11,19,6,5,11,8,19,9,4,13,17,6,23,29,4,3,7,2,3,5,4,3}, 1,9,34,{1,9,2,11,13,8,3,11,2,13,3,8,11,19,6,5,11,8,19,9,4,13,17,6,23,29,4,3,7,2,3,5,4,3}, 1,10,10,{1,10,11,3,2,5,7,4,11,3}. Even exotic seeds give no long sequences, e.g. 967,3000,24,{967,3000,3967,6967,154,7121,75,28,103,131,18,149,167,4,9,13,2,3,5,4,3,7,2,3}. For a(1)=1, maximal length = 55 is found for a(2)=1207: 1,1207,55,{1,1207,8,243,251,26,277,3,40,43,83,18,101,7,36,43,79,2,27,29,8,37,9,2,11,13,8,3,11,2,13,3,8,11,19,6,5,11,8,19,9,4,13,17,6,23,29,4,3,7,2,3,5,4,3}.
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