

A191060


Primes that are not squares mod 11.


3



2, 7, 13, 17, 19, 29, 41, 43, 61, 73, 79, 83, 101, 107, 109, 127, 131, 139, 149, 151, 167, 173, 193, 197, 211, 227, 233, 239, 241, 263, 271, 277, 281, 283, 293, 307, 337, 347, 349, 359, 373, 409, 431, 439, 457, 461, 479, 491, 503, 523, 541, 547, 557, 563
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OFFSET

1,1


COMMENTS

Inert rational primes in the field Q(sqrt(11)).  N. J. A. Sloane, Dec 25 2017
These are also the primes p for which the polynomial x^3  x^2  x  1 (mod p) has only one integer root. This is important for the Fibonacci and Lucas 3step recursions, A000073 and A001644. See A106276.  T. D. Noe, Apr 17 2012
It appears that these are the primes p such that the sequence p^(5*n) mod 11 has period length 2, repeating [1, 10].  Gary Detlefs, May 18 2014


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index to sequences related to decomposition of primes in quadratic fields


MATHEMATICA

Select[Prime[Range[200]], JacobiSymbol[#, 11] == 1 &]


PROG

(MAGMA) [p: p in PrimesUpTo(563)  JacobiSymbol(p, 11) eq 1]; // Vincenzo Librandi, Sep 11 2012


CROSSREFS

Sequence in context: A196012 A065104 A138645 * A166246 A250185 A063206
Adjacent sequences: A191057 A191058 A191059 * A191061 A191062 A191063


KEYWORD

nonn,easy


AUTHOR

T. D. Noe, May 25 2011


STATUS

approved



