A089986 -id:A089986 - cp's OEIS frontend

A111199 Numbers k such that 4k + 9 is prime.

1, 2, 5, 7, 8, 11, 13, 16, 20, 22, 23, 25, 26, 32, 35, 37, 41, 43, 46, 47, 55, 56, 58, 62, 65, 67, 68, 71, 76, 77, 82, 85, 86, 91, 95, 97, 98, 100, 103, 106, 110, 112, 113, 125, 128, 133, 137, 140, 142, 146, 148, 151, 152, 158, 161, 163, 166, 167, 173, 175, 181, 187

Offset: 1

Parthasarathy Nambi, Oct 24 2005

nonn

			For k=98, 4*k + 9 = 401 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A005098, A095278, A089986, A153238, A144562.

is(n)=isprime(4*n+9) \\ Charles R Greathouse IV, Feb 20 2017

a(n) = A005098(n+1) - 2. - R. J. Mathar, Sep 23 2009

More terms from R. J. Mathar, Sep 23 2009

A152843 Numbers n such that both 2n+3 and 4n+7 are prime.

Original entry on oeis.org

0, 1, 4, 10, 13, 19, 25, 40, 43, 55, 64, 85, 88, 94, 115, 118, 124, 139, 145, 178, 208, 214, 220, 244, 253, 295, 319, 325, 328, 340, 358, 370, 379, 403, 454, 475, 505, 508, 514, 523, 550, 610, 613, 643, 703, 718, 724, 739, 748, 754, 778, 790, 799, 865, 904, 943

Offset: 1

Vincenzo Librandi, Dec 14 2008

Or, numbers n such that 2n+3 is a Sophie Germain prime. [Klaus Brockhaus, Dec 22 2008]

			For n = 10, 2*n+3 = 23 is prime and 4*n+7 = 47 is prime. 23 = A005384(5).

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

Cf. A067076 (2n+3 is prime), A089986 (4n+7 is prime), A005384 (Sophie Germain primes).

[ n: n in [0..1000] | IsPrime(2*n+3) and IsPrime(4*n+7) ];

Join[{0}, Select[Range[1000], PrimeQ[2*#+3] && PrimeQ[4*#+7] &]] (* Vincenzo Librandi, Aug 30 2012 *)
Select[Range[0,1000],AllTrue[{2#+3,4#+7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 07 2015 *)

Edited and extended by Klaus Brockhaus, Dec 22 2008

A023215 Primes p such that 4*p + 7 is also prime.

Original entry on oeis.org

3, 13, 19, 31, 43, 61, 103, 109, 139, 163, 241, 271, 313, 373, 379, 499, 523, 601, 613, 631, 643, 673, 709, 733, 739, 751, 769, 811, 823, 829, 883, 1021, 1033, 1051, 1063, 1069, 1129, 1171, 1231, 1249, 1291, 1381, 1459, 1483, 1531, 1549, 1579, 1621, 1663

Offset: 1

David W. Wilson

Except for the first term, all terms are congruent to 1 (mod 6). - John Cerkan, Sep 07 2016

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

Subsequence of primes of A089986.

[n: n in PrimesUpTo(500) | IsPrime(4*n+7)]; // Vincenzo Librandi, Nov 19 2010

A023215:=n->`if`(isprime(n) and isprime(4*n+7), n, NULL): seq(A023215(n), n=1..3*10^3); # Wesley Ivan Hurt, Sep 07 2016

Select[Prime[Range[300]],PrimeQ[4#+7]&] (* Harvey P. Dale, Jan 21 2011 *)

A153086 Numbers n such that 4*n+7 is not prime.

Original entry on oeis.org

2, 5, 7, 8, 11, 12, 14, 17, 20, 21, 22, 23, 26, 27, 28, 29, 32, 34, 35, 37, 38, 41, 42, 44, 45, 47, 49, 50, 52, 53, 56, 57, 59, 60, 62, 63, 65, 67, 68, 70, 71, 72, 73, 74, 77, 78, 79, 80, 82, 83, 84, 86, 87, 89, 91, 92, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 107

Offset: 1

Vincenzo Librandi, Dec 18 2008

			*;
2, *;
*, 7, *;
5, *, 14, *;
*, 12, *, 23, *;
8, *, 21, *, 34, *;
*, 17, *, 32, *, 47, *; etc.
where * marks the non-integer values of (2*n*k + k + n - 3)/2 with n >= k >= 1. - _Vincenzo Librandi_, Nov 21 2012

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

Cf. A089986, A153053.

[n: n in [1..120] | not IsPrime(4*n + 7)]; // Vincenzo Librandi, Nov 21 2012

Select[Range[200], !PrimeQ[4# + 7] &] (* Vincenzo Librandi, Nov 21 2012 *)

cp's OEIS Frontend

A111199 Numbers k such that 4k + 9 is prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions

A152843 Numbers n such that both 2n+3 and 4n+7 are prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Extensions

A023215 Primes p such that 4*p + 7 is also prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

A153086 Numbers n such that 4*n+7 is not prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica