A102656 -id:A102656 - cp's OEIS frontend

A141849 Primes congruent to 1 mod 11.

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

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Primes congruent to 1 mod 22. - Chai Wah Wu, Apr 28 2025

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

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)).

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

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

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

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

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

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

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

A102731 Numbers k such that 11*k + 23 is prime.

Original entry on oeis.org

0, 4, 6, 16, 28, 30, 34, 36, 40, 54, 58, 60, 64, 76, 78, 84, 88, 90, 100, 114, 118, 126, 130, 144, 160, 168, 180, 186, 190, 196, 204, 208, 210, 214, 216, 228, 240, 244, 246, 258, 264, 268, 274, 286, 288, 294, 298, 300, 306, 310, 316, 328, 334, 336, 348, 354, 364

Offset: 1

Parthasarathy Nambi, Feb 07 2005

			If k=0, then 11*0 + 23 = 23 (prime).
If k=54, then 11*54 + 23 = 617 (prime).
If k=114, then 11*114 + 23 = 1277 (prime).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

[n: n in [0..1000] | IsPrime(11*n + 23)]; // Vincenzo Librandi, Nov 17 2010

Select[Range[0,400],PrimeQ[11#+23]&] (* Harvey P. Dale, Oct 17 2011 *)

is(n)=isprime(11*n+23) \\ Charles R Greathouse IV, Jun 12 2017

a(n) = A102656(n) - 2. - R. J. Mathar, Jul 08 2009

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A141849 Primes congruent to 1 mod 11.

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A102731 Numbers k such that 11*k + 23 is prime.

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