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A141849 Primes congruent to 1 mod 11.

%I A141849 #65 Apr 29 2025 04:53:48
%S A141849 23,67,89,199,331,353,397,419,463,617,661,683,727,859,881,947,991,
%T A141849 1013,1123,1277,1321,1409,1453,1607,1783,1871,2003,2069,2113,2179,
%U A141849 2267,2311,2333,2377,2399,2531,2663,2707,2729,2861,2927,2971,3037,3169,3191,3257
%N A141849 Primes congruent to 1 mod 11.
%C A141849 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
%C A141849 Primes congruent to 1 mod 22. - _Chai Wah Wu_, Apr 28 2025
%H A141849 Vincenzo Librandi, <a href="/A141849/b141849.txt">Table of n, a(n) for n = 1..1000</a>
%F A141849 a(n) ~ 10n log n. - _Charles R Greathouse IV_, Jul 02 2016
%p A141849 a:=select(n->isprime(n) and modp(n,11)=1,[$1..4000]); # _Muniru A Asiru_, Apr 19 2018
%t A141849 Select[Range[1,10000,11],PrimeQ] (* _Vladimir Joseph Stephan Orlovsky_, May 18 2011 *)
%o A141849 (Magma) [ p: p in PrimesUpTo(5000) | p mod 11 eq 1 ]; // _Vincenzo Librandi_, Apr 19 2011
%o A141849 (PARI) is(n)=isprime(n) && n%11==1 \\ _Charles R Greathouse IV_, Jul 01 2016
%o A141849 (PARI) forstep(n=2, 1e3, 2, if(isprime(p=11*n+1), print1(p, ", "))); \\ _Altug Alkan_, Apr 19 2018
%o A141849 (GAP) Filtered([1..4000],n->n mod 11=1 and IsPrime(n)); # _Muniru A Asiru_, Apr 19 2018
%Y A141849 Cf. A000040, A090187, A102656.
%Y A141849 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).
%Y A141849 Cf. A034694 (smallest prime == 1 (mod n)).
%Y A141849 Cf. A038700 (smallest prime == n-1 (mod n)).
%Y A141849 Cf. A038026 (largest possible value of smallest prime == r (mod n)).
%K A141849 nonn,easy
%O A141849 1,1
%A A141849 _N. J. A. Sloane_, Jul 11 2008