A095278 -id:A095278 - cp's OEIS frontend

A094897 If 4n+1 is not prime and 4n+3 is prime then a(n)=4*n+3, else a(n)=0.

3, 0, 11, 0, 0, 23, 0, 0, 0, 0, 0, 47, 0, 0, 59, 0, 67, 71, 0, 79, 83, 0, 0, 0, 0, 0, 107, 0, 0, 0, 0, 127, 131, 0, 0, 0, 0, 0, 0, 0, 163, 167, 0, 0, 179, 0, 0, 191, 0, 0, 0, 0, 211, 0, 0, 223, 227, 0, 0, 239, 0, 0, 251, 0, 0, 263, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 307, 311, 0, 0, 0, 0, 331, 0

Offset: 0

Roger L. Bagula, Jun 14 2004

nonn

Cf. A045751, A095278, A094896.

[IsPrime(4*n+3) and not IsPrime(4*n+1) select 4*n+3 else 0:n in [0..85]]; // Marius A. Burtea, Nov 15 2019

A094897 := proc(n)
    if not isprime(4*n+1) and isprime(4*n+3) then
        4*n+3;
    else
        0;
    end if;
end proc:
seq(A094897(n),n=0..86) ; # R. J. Mathar, Nov 15 2019

a=Table[If[PrimeQ[4*n+1]==False&&PrimeQ[4*n+3]==True, 4*n+3, 0], {n, 0, 200}]

A126955 Numbers n such that 2n+1, 3n+2 and 4n+3 are primes.

Original entry on oeis.org

1, 5, 65, 89, 119, 215, 455, 755, 779, 965, 1175, 1349, 1409, 1469, 1679, 1745, 1769, 1889, 1955, 2009, 2105, 2435, 2519, 2525, 2585, 2639, 4685, 5045, 5165, 5735, 5915, 5969, 6725, 7415, 7469, 7895, 8045, 9065, 9365, 9449, 9659, 9779, 9959, 10379

Offset: 1

J. M. Bergot, Mar 19 2007

nonn

			Take n = 89. Then 2*89 + 1 = 179, 3*89 + 2 = 269 and 4*89 + 3 = 359 are primes.

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

Intersection of A005097, A024893, A095278. Cf. A126956.

Select[Range[10500], PrimeQ[2# + 1] && PrimeQ[3# + 2] && PrimeQ[4# + 3] &] (* Ray Chandler, Mar 20 2007 *)
Select[Range[11000],AllTrue[{2#+1,3#+2,4#+3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 23 2017 *)

Extended by Ray Chandler, Robert G. Wilson v and Stuart Clary, Mar 20 2007

A156287 Numbers k such that 4*k-5 is a prime number.

Original entry on oeis.org

2, 3, 4, 6, 7, 9, 12, 13, 16, 18, 19, 21, 22, 27, 28, 33, 34, 36, 39, 42, 43, 46, 49, 51, 54, 57, 58, 61, 64, 67, 69, 72, 78, 79, 84, 88, 91, 93, 96, 97, 106, 109, 111, 112, 117, 118, 121, 123, 124, 126, 127, 132, 138, 142, 144, 148, 151, 153, 156, 159, 162, 163, 166

Offset: 1

Vincenzo Librandi, Feb 07 2009

Two more than the associated A095278, one more than the associated A005099. - R. J. Mathar, Jan 05 2011

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

Cf. A156288, A005099, A095278.

[n: n in [1..400] | IsPrime(4*n - 5)]; // Vincenzo Librandi, Feb 16 2013

Select[Range[600], PrimeQ[4 # - 5]&] (* Vincenzo Librandi, Feb 16 2013 *)

A023250 Primes that remain prime through 2 iterations of function f(x) = 4x + 3.

Original entry on oeis.org

2, 7, 11, 37, 67, 89, 109, 149, 179, 257, 439, 467, 571, 677, 691, 719, 929, 977, 1019, 1279, 1381, 1447, 1549, 1567, 1747, 1787, 1901, 1931, 2111, 2161, 2207, 2287, 2347, 2377, 2459, 2539, 2671, 2711, 2819, 3119, 3229, 3371, 3491, 3607, 3637, 3821, 3877

Offset: 1

David W. Wilson

nonn

Primes p such that 4*p+3 and 16*p+15 are also primes. - Vincenzo Librandi, Aug 04 2010

John Cerkan, Table of n, a(n) for n = 1..10000

Subsequence of A095278.

[n: n in [0..100000] | IsPrime(n) and IsPrime(4*n+3) and IsPrime(16*n+15)]; // Vincenzo Librandi, Aug 04 2010

A023250:=n->`if`(isprime(n) and isprime(4*n+3) and isprime(16*n+15), n, NULL): seq(A023250(n), n=1..10^4); # Wesley Ivan Hurt, Feb 12 2017

Select[Range@ 3900, Times @@ Boole@ PrimeQ@ NestList[4 # + 3 &, #, 2] > 0 &] (* Michael De Vlieger, Sep 13 2016 *)

A105134 Numbers n such that 16n+9 is prime.

Original entry on oeis.org

2, 4, 5, 8, 14, 17, 19, 25, 28, 32, 35, 37, 38, 47, 50, 53, 58, 59, 64, 65, 68, 70, 74, 80, 82, 89, 92, 100, 103, 107, 109, 112, 119, 124, 130, 133, 134, 142, 143, 148, 149, 152, 154, 157, 163, 164, 169, 170, 173, 178, 184, 185, 187, 190, 200, 203, 214, 215, 220, 224, 229

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

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

Cf. A095278, A105133-A105140, A002145, A007521, A105126-A105132.

[n: n in [0..500] | IsPrime(16*n+9)]; // Vincenzo Librandi, Jan 07 2013

Select[Range[0, 500], PrimeQ[16 # + 9]&] (* Vincenzo Librandi, Jan 07 2013 *)

is(n)=isprime(16*n+9) \\ Charles R Greathouse IV, Jun 06 2017

A105138 Numbers n such that 256n+129 is prime.

Original entry on oeis.org

2, 4, 5, 10, 13, 17, 19, 25, 28, 37, 38, 40, 44, 47, 52, 53, 59, 62, 70, 74, 77, 79, 82, 83, 103, 110, 115, 119, 124, 130, 137, 140, 149, 152, 158, 170, 173, 178, 179, 193, 200, 205, 208, 209, 212, 217, 230, 235, 238, 242, 247, 248, 257, 268, 269, 272, 275, 280, 283, 299, 307

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

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

Cf. A095278, A105133-A105140, A002145, A007521, A105126-A105132.

[n: n in [0..350] | IsPrime(256*n+129)]; // Vincenzo Librandi, Jan 08 2013

Select[Range[0, 500], PrimeQ[256 # + 129]&] (* Vincenzo Librandi, Jan 08 2013 *)

is(n)=isprime(256*n+129) \\ Charles R Greathouse IV, Jun 12 2017

A105139 Numbers k such that 512*k+257 is prime.

Original entry on oeis.org

0, 1, 6, 15, 18, 27, 28, 43, 45, 52, 60, 61, 70, 73, 78, 81, 85, 90, 96, 97, 111, 112, 117, 138, 147, 151, 153, 165, 172, 178, 187, 192, 196, 202, 208, 210, 211, 213, 216, 222, 228, 231, 235, 243, 250, 252, 253, 255, 262, 265, 270, 280, 291, 298, 301, 312, 325, 328, 330, 337

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

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

Cf. A095278, A105133-A105140, A002145, A007521, A105126-A105132.

[n: n in [0..350] | IsPrime(512*n + 257)]; // Vincenzo Librandi, Jan 08 2013

Select[Range[0, 500], PrimeQ[512 # + 257]&] (* Vincenzo Librandi, Jan 08 2013 *)

is(n)=isprime(512*n+257) \\ Charles R Greathouse IV, Jun 06 2017

A106068 Primes p such that 3p + 4 and 4p + 3 are primes.

Original entry on oeis.org

5, 11, 19, 31, 41, 59, 89, 109, 151, 179, 181, 229, 241, 331, 349, 389, 439, 509, 521, 599, 661, 719, 769, 839, 881, 929, 1019, 1039, 1129, 1229, 1291, 1409, 1451, 1481, 1549, 1669, 1741, 1759, 1801, 1811, 2111, 2131, 2539, 2621, 2671, 2699, 2819, 2879

Offset: 1

Zak Seidov, May 07 2005

nonn

Prime terms in A124855.

Marius A. Burtea, Table of n, a(n) for n = 1..534

Cf. A034936, A095278, A124855.

[p: p in PrimesUpTo(5000)|IsPrime(3*p+4) and IsPrime(4*p+3)] // Vincenzo Librandi, Jan 30 2011

Select[Prime[Range[450]], PrimeQ[4#+3]&&PrimeQ[3#+4]&]

isok(p) = isprime(p) && isprime(3*p+4) && isprime(4*p+3); \\ Michel Marcus, Oct 12 2018

Extended by Ray Chandler, Mar 14 2007

A126330 Primes of the form 4p+3 where p is a prime.

Original entry on oeis.org

11, 23, 31, 47, 71, 79, 127, 151, 167, 191, 239, 271, 359, 431, 439, 599, 607, 631, 719, 727, 911, 919, 967, 1031, 1087, 1231, 1327, 1399, 1439, 1471, 1559, 1607, 1759, 1831, 1847, 1871, 1951, 1999, 2039, 2087, 2287, 2311, 2351, 2399, 2591, 2647, 2711, 2767

Offset: 1

J. M. Bergot, Mar 09 2007

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

For the primes p see A023213.

Cf. A002145, A004767, A080148, A090866, A095278.

select(p -> isprime(p) and isprime((p-3)/4), [seq(p,p=7..10000,4)]); # Robert Israel, Aug 08 2019

Select[3 + 4Prime@Range[130], PrimeQ] (* Ray Chandler, Jun 29 2008 *)

Checked and extended by N. J. A. Sloane, Mar 10 2007

A126956 Numbers n such that 3n+2, 4n+3 and 5n+4 are primes.

Original entry on oeis.org

5, 17, 77, 89, 119, 185, 257, 287, 395, 665, 755, 797, 929, 1175, 1259, 1337, 1379, 1445, 1469, 1769, 2057, 2105, 3125, 3419, 3437, 3629, 3815, 3989, 4079, 4157, 4175, 4217, 4367, 4445, 4847, 5045, 5375, 6089, 6137, 6167, 6359, 6419, 6485, 6725, 6887

Offset: 1

J. M. Bergot, Mar 19 2007

nonn

			Take n = 185. Then 3*185 + 2 = 557, 4*185 + 3 = 743 and 5*185 + 4 = 929 are primes.

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

Intersection of A024893, A095278, A024897. Cf. A126955.

Select[Range[7000], PrimeQ[3# + 2] && PrimeQ[4# + 3] && PrimeQ[5# + 4] &] (* Ray Chandler, Mar 20 2007 *)
Select[Range[7000],AllTrue[{3#+2,4#+3,5#+4},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 06 2019 *)

Corrected and extended by Ray Chandler, Stuart Clary, Robert G. Wilson v and Zak Seidov, Mar 20 2007

cp's OEIS Frontend

A094897 If 4*n+1 is not prime and 4*n+3 is prime then a(n)=4*n+3, else a(n)=0.

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Magma

Maple

Mathematica

A126955 Numbers n such that 2n+1, 3n+2 and 4n+3 are primes.

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Examples

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Programs

Mathematica

Extensions

A156287 Numbers k such that 4*k-5 is a prime number.

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Author

Keywords

Comments

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Crossrefs

Programs

Magma

Mathematica

A023250 Primes that remain prime through 2 iterations of function f(x) = 4x + 3.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

A105134 Numbers n such that 16n+9 is prime.

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Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A105138 Numbers n such that 256n+129 is prime.

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Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A105139 Numbers k such that 512*k+257 is prime.

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Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A106068 Primes p such that 3p + 4 and 4p + 3 are primes.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

A094897 If 4n+1 is not prime and 4n+3 is prime then a(n)=4*n+3, else a(n)=0.