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Numbers n such that 11*n + 17 is prime.
+10
1
0, 4, 6, 10, 12, 16, 24, 30, 40, 42, 46, 60, 66, 70, 72, 76, 82, 84, 94, 100, 112, 124, 130, 142, 144, 150, 156, 160, 174, 180, 186, 192, 202, 214, 216, 220, 222, 226, 234, 240, 250, 252, 256, 282, 286, 292, 294, 304, 312, 322, 324, 334, 342, 346, 352, 354, 364
EXAMPLE
If n=0, then 11*n + 17 = 17 (prime).
If n=42, then 11*n + 17 = 479 (prime).
MAPLE
a:=proc(n) if isprime(11*n+17)=true then n else fi end: seq(a(n), n=0..420); # Emeric Deutsch, Jun 26 2005
MATHEMATICA
Select[Range[0, 500], PrimeQ[11#+17]&] (* Harvey P. Dale, Oct 16 2014 *)
Numbers n such that 11*n + 19 is prime.
+10
1
0, 2, 8, 12, 14, 20, 24, 30, 44, 48, 50, 54, 62, 72, 78, 90, 92, 98, 104, 110, 122, 128, 132, 134, 140, 150, 162, 164, 168, 170, 174, 180, 188, 192, 194, 212, 218, 230, 234, 240, 252, 258, 260, 272, 282, 288, 290, 294, 300, 308, 318, 320, 324, 332, 344, 348, 362
EXAMPLE
If n=0, then 11*n + 19 = 19 (prime).
If n=48, then 11*n + 19 = 547 (prime).
MAPLE
a:=proc(n) if isprime(11*n+19)=true then n else fi end: seq(a(n), n=0..400); # Emeric Deutsch, Jul 04 2005
MATHEMATICA
Select[Range[0, 400, 2], PrimeQ[ 11#+19]&] (* Harvey P. Dale, Jan 05 2019 *)
Numbers n such that 11*n + 29 is prime.
+10
1
0, 4, 10, 18, 22, 24, 28, 30, 42, 48, 52, 64, 72, 78, 84, 88, 90, 94, 100, 102, 108, 114, 118, 130, 132, 144, 148, 154, 160, 162, 168, 178, 184, 192, 198, 202, 204, 210, 214, 238, 244, 252, 270, 280, 298, 300, 304, 312, 318, 322, 324, 328, 330, 340, 354, 358
COMMENTS
Two less than the associated entry in A102711.
EXAMPLE
If n=0, then 11*n + 29 = 29 (prime).
If n=48, then 11*n + 29 = 557 (prime).
MAPLE
a:=proc(n) if isprime(11*n+29)=true then n else fi end: seq(a(n), n=0..400); # Emeric Deutsch, Jun 26 2005
MATHEMATICA
Select[Range[0, 400], PrimeQ[11#+29]&] (* Harvey P. Dale, Jan 26 2013 *)
Numbers n such that 11*n + 31 is prime.
+10
1
0, 2, 6, 12, 18, 20, 26, 32, 38, 56, 60, 66, 72, 80, 86, 90, 96, 98, 102, 116, 122, 128, 132, 138, 140, 146, 156, 168, 170, 180, 188, 192, 206, 210, 222, 228, 240, 242, 252, 266, 270, 272, 276, 278, 290, 300, 312, 318, 326, 336, 342, 350, 356, 362, 366, 368, 380
EXAMPLE
If n=0, then 11*n + 31 = 31 (prime).
If n=56, then 11*n + 31 = 647 (prime).
MAPLE
a:=proc(n) if isprime(11*n+31)=true then n else fi end: seq(a(n), n=0..450); # Emeric Deutsch, Jun 26 2005
MATHEMATICA
Select[Range[0, 400], PrimeQ[11#+31]&] (* Harvey P. Dale, Nov 02 2011 *)
Numbers n such that 11*n+5 is not prime.
+10
1
1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81, 83, 85, 86, 87, 88
EXAMPLE
Distribution of the even terms in the following triangular array:
*;
*,*;
*,*,4;
2,*,*,*;
*,*,*,*,*;
*,*,*,*,*,*;
*,*,*,*,*,*,20;
*,*,*,*,*,*,*,*,;
*,*,*,*,*,22,*,*,*;
*,*,*,*,*,*,*,32,*,*;
*,10,*,*,*,*,*,*,*,*,*;
*,*,*,20,*,*,*,*,*,*,*,*;
*,*,*,*,*,*,*,*,*,*,56,*,*:
*,*,18,*,*,*,*,*,*,*,*,*,*,76;
8,*,*,*,*,*,*,*,*,*,*,70,*,*,*; etc.
where * marks the non-integer values of (4*h*k + 2*k + 2*h - 4)/11 with h >= k >= 1. - Vincenzo Librandi, Jan 17 2013
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