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
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)).
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 11 2008
STATUS
approved