A000923 Primes p of the form 3k+1 such that sum_{x=1..p} cos(2*Pi*x^3/p) < -sqrt(p). (Formerly M5365 N2331)

97, 139, 151, 199, 211, 331, 433, 541, 547, 601, 607, 631, 751, 787, 937, 1039, 1063, 1249, 1321, 1327, 1381, 1471, 1483, 1663, 1693, 1741, 1747, 1879, 1999, 2113, 2143, 2377, 2437, 2503, 2521, 2557, 2593, 2677, 2797, 2857, 2887, 3019, 3121, 3313, 3331, 3361

Offset

1,1

References

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

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

D. R. Heath-Brown, Kummer's Conjecture for Cubic Gauss Sums

Example

97 is here because the sum of cos(2*Pi*x^3/97) = -11.3259 < -sqrt(97).

Crossrefs

Cf. A000921, A000922, A002476.

Sequence in context: A258877 A073076 A157213 * A142528 A139500 A344481

Adjacent sequences: A000920 A000921 A000922 * A000924 A000925 A000926

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by Don Reble, May 26 2007

Status

approved