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%I M2737 N1099 #37 Oct 19 2017 10:48:40
%S 3,8,20,44,80,343,288,608,1023,2848,4095,40959,16383,32768,11375,
%T 655360,262143,3670016,1048575,2097151
%N Maximum m such that there are no two adjacent elements belonging to the same n-th power residue class modulo some prime p in the sequence 1,2,...,m (equivalently, there is no n-th power residue modulo p in the sequence 1/2,2/3,...,(m-1)/m).
%C Rabung and Jordan (1970) incorrectly computed a(8) as 399: their placement of residues supporting a(8)=399 fails since 80 and 81 fall into the same 8th-power residue class. - _Max Alekseyev_, Aug 10 2005
%C _Don Reble_ pointed out that for even n, the n-th residue class placement of prime factors q of n must obey the quadratic reciprocity law: q must be in an even class whenever n*(q-1) is a multiple of 8. - _Max Alekseyev_, Sep 04 2017
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. H. Jordan, <a href="http://dx.doi.org/10.4153/CJM-1964-030-6">Pairs of consecutive power residues or nonresidues</a>, Canad. J. Math., 16 (1964), 310-314.
%H J. R. Rabung and J. H. Jordan, <a href="http://dx.doi.org/10.1090/S0025-5718-1970-0277469-8">Consecutive power residues or nonresidues</a>, Math. Comp., 24 (1970), 737-740.
%F If 8|n, a(n) >= 2^(n/2) - 1; otherwise a(n) >= 2^n - 1. - _Max Alekseyev_, Aug 10 2005; corrected Sep 04, 2017.
%Y Cf. A000445, A111931.
%K nonn,more
%O 2,1
%A _N. J. A. Sloane_
%E a(8) corrected and a(9)-a(16) added by _Max Alekseyev_, Aug 10 2005
%E a(8), a(10), a(16) corrected, and a(17)-a(21) added by _Don Reble_, communicated by _Max Alekseyev_, Sep 04 2017
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