A155723
Numbers k such that 2*k + 9 is not prime.
Original entry on oeis.org
0, 3, 6, 8, 9, 12, 13, 15, 18, 20, 21, 23, 24, 27, 28, 30, 33, 34, 36, 38, 39, 41, 42, 43, 45, 48, 51, 53, 54, 55, 56, 57, 58, 60, 62, 63, 66, 67, 68, 69, 72, 73, 75, 76, 78, 80, 81, 83, 84, 87, 88, 89, 90, 93, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 108, 111, 113, 114
Offset: 1
Distribution of the terms in the following triangular array:
0;
3, 8;
6, 13, 20;
9, 18, 27, 36;
12, 23, 34, 45, 56;
15, 28, 41, 54, 67, 80;
18, 33, 48, 63, 78, 93, 108;
21, 38, 55, 72, 89, 106, 123, 140;
24, 43, 62, 81, 100, 119, 138, 157, 176;
27, 48, 69, 90, 111, 132, 153, 174, 195, 216;
30, 53, 76, 99, 122, 145, 168, 191, 214, 237, 260;
33, 58, 83, 108, 133, 158, 183, 208, 233, 258, 283, 308;
36, 63, 90, 117, 144, 171, 198, 225, 252, 279, 306, 333, 360;
etc.
the values of (2*h*k + k + h - 4) with h >= k >= 1. - _Vincenzo Librandi_, Jan 16 2013
A023245
Primes that remain prime through 2 iterations of the function f(x) = 2x + 9.
Original entry on oeis.org
5, 11, 19, 31, 59, 61, 71, 101, 109, 151, 179, 239, 241, 269, 281, 389, 409, 439, 449, 521, 571, 641, 659, 719, 829, 911, 971, 1051, 1061, 1181, 1201, 1229, 1319, 1361, 1439, 1579, 1669, 1699, 1741, 1831, 1949, 2269, 2341, 2371, 2521, 2549, 2579, 2609, 2671
Offset: 1
-
[n: n in [0..100000] | IsPrime(n) and IsPrime(2*n+9) and IsPrime(4*n+27)] // Vincenzo Librandi, Aug 04 2010
-
Select[Prime[Range[500]],And@@PrimeQ[Rest[NestList[2#+9&,#,2]]]&] (* Harvey P. Dale, Mar 23 2011 *)
-
isok(n) = isprime(n) && isprime(2*n+9) && isprime(4*n+27); \\ Michel Marcus, Sep 12 2016
A023276
Primes that remain prime through 3 iterations of function f(x) = 2x + 9.
Original entry on oeis.org
5, 11, 31, 71, 281, 521, 911, 1181, 2371, 2521, 3391, 3701, 4211, 4931, 5051, 7211, 7411, 8221, 8431, 8461, 8501, 8641, 8951, 9601, 9871, 10301, 11981, 12421, 13121, 13921, 14591, 16381, 16451, 16901, 16931, 17791, 17881, 19391, 19751, 21991, 23021
Offset: 1
-
[n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+9) and IsPrime(4*n+27) and IsPrime(8*n+63)] // Vincenzo Librandi, Aug 04 2010
-
A023276:=n->`if`(isprime(n) and isprime(2*n+9) and isprime(4*n+27) and isprime(8*n+63), n, NULL): seq(A023276(n), n=1..10^5); # Wesley Ivan Hurt, Feb 11 2017
-
Select[Prime@ Range@ 2600, Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 9 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 19 2016 *)
Select[Prime[Range[3000]],AllTrue[Rest[NestList[2#+9&,#,3]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 01 2017 *)
-
is(n)=isprime(n) && isprime(2*n+9) && isprime(4*n+27) && isprime(8*n+63) \\ Charles R Greathouse IV, Sep 20 2016
A288246
Numbers k such that 8*k^3 + 81 is prime.
Original entry on oeis.org
1, 4, 8, 10, 11, 13, 20, 26, 29, 34, 35, 43, 46, 50, 53, 56, 68, 70, 71, 85, 86, 94, 95, 98, 125, 130, 131, 139, 149, 154, 160, 161, 163, 169, 170, 178, 184, 194, 196, 199, 208, 215, 229, 239, 259, 266, 269, 271, 280, 283, 286, 290, 298, 305, 313
Offset: 1
a(1) = 1 because 8*1 + 81 = 89 is prime.
a(2) = 4 because 8*4^3 + 81 = 593 is prime.
Cf.
A155722: Numbers k such that 2*k + 9 is prime.
Cf.
A002971: Numbers k such that 4*k^2 + 25 is prime.
Comments