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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 (list; graph; refs; listen; history; text; internal format)
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 3-step 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

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Last modified April 16 11:10 EDT 2021. Contains 343037 sequences. (Running on oeis4.)