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Primes p of the form 3k+1 such that -sqrt(p) < sum_{x=1..p} cos(2*Pi*x^3/p) < sqrt(p).
(Formerly M4890 N2096)
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%I M4890 N2096 #21 Oct 19 2017 03:13:42

%S 13,19,37,61,109,157,193,241,283,367,373,379,397,487,571,613,619,733,

%T 739,859,883,907,1009,1033,1051,1129,1153,1201,1291,1297,1303,1399,

%U 1429,1453,1459,1489,1549,1669,1699,1753,1783,1831,1861,1933,1951,1987,2011

%N Primes p of the form 3k+1 such that -sqrt(p) < sum_{x=1..p} cos(2*Pi*x^3/p) < sqrt(p).

%D H. Hasse, Vorlesungen über Zahlentheorie. Springer-Verlag, NY, 1964, p. 482.

%D G. B. Mathews, Theory of Numbers, 2nd edition. Chelsea, NY, p. 228.

%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 T. D. Noe, <a href="/A000922/b000922.txt">Table of n, a(n) for n = 1..1000</a>

%H D. R. Heath-Brown, <a href="http://eprints.maths.ox.ac.uk/158/01/kummer.pdf">Kummer's Conjecture for Cubic Gauss Sums</a>

%e 13 is here because the sum of cos(2*Pi*x^3/13) = 1.8217, between -sqrt(13) and +sqrt(13).

%Y Cf. A000921, A000923, A002476.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E Edited by _Don Reble_, May 26 2007