Thread: A113767
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Old 2018-04-12, 08:45   #4
10metreh's Avatar
Nov 2008

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It feels like these sequences ought to be finite. The only long-term modular restriction I can think of for members of the sequence is that they cannot be 1 mod p for any p other than 2 and the previous term (correct me if I've missed something!). Since 78557 has covering set {3, 5, 7, 13, 19, 37, 73}, 78557+3*5*7*13*19*37*73*n is a Sierpinski number for every n, and 78557 is not 1 mod any of the primes in its covering set, so eventually the sequence ought to hit a number of this form, if it does not hit another Sierpinski number first.
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