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A141849 Primes congruent to 1 mod 11. 8
23, 67, 89, 199, 331, 353, 397, 419, 463, 617, 661, 683, 727, 859, 881, 947, 991, 1013, 1123, 1277, 1321, 1409, 1453, 1607, 1783, 1871, 2003, 2069, 2113, 2179, 2267, 2311, 2333, 2377, 2399, 2531, 2663, 2707, 2729, 2861, 2927, 2971, 3037, 3169, 3191, 3257 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: Also primes p such that ((x+1)^11-1)/x has 10 distinct irreducible factors of degree 1 over GF(p). - Federico Provvedi, Apr 17 2018

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) ~ 10n log n. - Charles R Greathouse IV, Jul 02 2016

MAPLE

a:=select(n->isprime(n) and modp(n, 11)=1, [$1..4000]); # Muniru A Asiru, Apr 19 2018

MATHEMATICA

Select[Range[1, 10000, 11], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 18 2011 *)

PROG

(MAGMA) [ p: p in PrimesUpTo(5000) | p mod 11 eq 1 ]; // Vincenzo Librandi, Apr 19 2011

(PARI) is(n)=isprime(n) && n%11==1 \\ Charles R Greathouse IV, Jul 01 2016

(PARI) forstep(n=2, 1e3, 2, if(isprime(p=11*n+1), print1(p, ", "))); \\ Altug Alkan, Apr 19 2018

(GAP) Filtered([1..4000], n->n mod 11=1 and IsPrime(n)); # Muniru A Asiru, Apr 19 2018

CROSSREFS

Cf. A000040, A090187, A102656.

Prime sequences A# (k,r) of the form k*n+r with 0 <= r <= k-1 (i.e., primes == r (mod k), or primes p with p mod k = r) and gcd(r,k)=1: A000040 (1,0), A065091 (2,1), A002476 (3,1), A003627 (3,2), A002144 (4,1), A002145 (4,3), A030430 (5,1), A045380 (5,2), A030431 (5,3), A030433 (5,4), A002476 (6,1), A007528 (6,5), A140444 (7,1), A045392 (7,2), A045437 (7,3), A045471 (7,4), A045458 (7,5), A045473 (7,6), A007519 (8,1), A007520 (8,3), A007521 (8,5), A007522 (8,7), A061237 (9,1), A061238 (9,2), A061239 (9,4), A061240 (9,5), A061241 (9,7), A061242 (9,8), A030430 (10,1), A030431 (10,3), A030432 (10,7), A030433 (10,9), this sequence (11,1), A090187 (11,2), A141850 (11,3), A141851 (11,4), A141852 (11,5), A141853 (11,6), A141854 (11,7), A141855 (11,8), A141856 (11,9), A141857 (11,10), A068228 (12,1), A040117 (12,5), A068229 (12,7), A068231 (12,11).

Cf. A034694 (smallest prime == 1 (mod n)).

Cf. A038700 (smallest prime == n-1 (mod n)).

Cf. A038026 (largest possible value of smallest prime == r (mod n)).

Sequence in context: A125872 A228611 A104945 * A125873 A059241 A241212

Adjacent sequences:  A141846 A141847 A141848 * A141850 A141851 A141852

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jul 11 2008

STATUS

approved

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Last modified June 25 22:27 EDT 2019. Contains 324364 sequences. (Running on oeis4.)