A000922 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)

13, 19, 37, 61, 109, 157, 193, 241, 283, 367, 373, 379, 397, 487, 571, 613, 619, 733, 739, 859, 883, 907, 1009, 1033, 1051, 1129, 1153, 1201, 1291, 1297, 1303, 1399, 1429, 1453, 1459, 1489, 1549, 1669, 1699, 1753, 1783, 1831, 1861, 1933, 1951, 1987, 2011

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

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

Crossrefs

Cf. A000921, A000923, A002476.

Sequence in context: A322923 A048523 A307627 * A107188 A029478 A252021

Adjacent sequences: A000919 A000920 A000921 * A000923 A000924 A000925

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by Don Reble, May 26 2007

Status

approved