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 A063980 Pillai primes: p such that there exists an integer m such that m!+1 is 0 mod p and p is not 1 mod m. 6
 23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, 227, 233, 239, 251, 257, 269, 271, 277, 293, 307, 311, 317, 359, 379, 383, 389, 397, 401, 419, 431, 449, 461, 463, 467, 479, 499, 503, 521, 557, 563, 569, 571, 577, 593, 599, 601, 607 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Hardy & Subbarao prove that this sequence is infinite. An upper bound can be extracted from their proof: a(n) < e^e^...^e^O(n log n) with e appearing n times. This tetrational bound could be improved with results on the disjointness of the factorizations of numbers of the form k! + 1. - Charles R Greathouse IV, Sep 15 2015 LINKS T. D. Noe and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) G. E. Hardy and M. V. Subbarao, A modified problem of Pillai and some related questions, Amer. Math. Monthly 109:6 (2002), pp. 554-559. MATHEMATICA ok[p_] := (r = False; Do[If[Mod[m! + 1, p] == 0 && Mod[p, m] != 1, r = True; Break[]], {m, 2, p}]; r); Select[Prime /@ Range[111], ok] (* Jean-François Alcover, Apr 22 2011 *) nn=1000; fact=1+Rest[FoldList[Times, 1, Range[nn]]]; t={}; Do[p=Prime[i]; m=2; While[m

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Last modified October 19 11:18 EDT 2020. Contains 337879 sequences. (Running on oeis4.)