cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A269259 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10 and p+2^12 are all primes.

Original entry on oeis.org

37, 163, 15667, 22093, 40177, 47287, 53593, 114577, 120607, 142543, 234067, 242377, 255907, 263047, 263803, 305407, 388117, 444607, 460387, 503287, 527143, 607093, 671353, 784897, 904663, 938947, 1063903, 1086493, 1172803, 1216807, 1233523, 1288543
Offset: 1

Views

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Keywords

Examples

			The prime 37 is in the sequence, since 37 + 16 = 53, 37 + 64 = 101, 37 + 256 = 293, 37 + 1024 = 1061 and 37 + 4096 = 4133 are all primes.
The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187 and 163 + 4096 = 4259 are all primes.

Links

Crossrefs

Subsequence of A269258.
Cf. A269257.

Programs

  • Magma
    [p: p in PrimesInInterval(2,1600000) | forall{i: i in [16,64,256,1024,4096] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016
  • Mathematica
    m = {2^4, 2^6, 2^8, 2^10, 2^12}; Select[Prime@ Range[2*10^5], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)
  • PARI
    is(n) = for(k=2, 6, if(!ispseudoprime(2^(2*k)+n), return(0))); return(1)
forprime(p=1, 16e5, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Jul 12 2016
  • Perl
    use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256,1024,4096); # Dana Jacobsen, Jul 13 2016

A269257 Primes p such that p+2^4, p+2^6 and p+2^8 are all primes.

Original entry on oeis.org

7, 37, 163, 337, 757, 967, 1033, 1303, 2293, 2377, 2647, 2713, 3607, 5023, 6763, 7417, 8677, 8803, 9157, 9277, 10273, 14683, 14827, 15313, 15667, 16417, 20113, 21163, 21757, 22093, 24907, 27043, 27763, 29803, 29863, 32173, 34897, 36793, 36997, 37783, 38287, 38977, 39607
Offset: 1

Views

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Keywords

Examples

			The prime 7 is in the sequence because 7+16 = 23, 7+64 = 71 and 7+256 = 263 are all primes.
The prime 37 is in the sequence because 37+16 = 53, 37+64 = 101 and 37+256 = 293 are all primes.

Links

Crossrefs

Subsequence of A002476, A049488, and A049490.

Programs

  • Mathematica
    Select[Prime[Range[10000]], PrimeQ[# + 2^4] && PrimeQ[# + 2^6] && PrimeQ[# + 2^8]&] (* Jean-François Alcover, Jul 12 2016 *)
With[{c=2^Range[4,8,2]},Select[Prime[Range[4200]],AllTrue[#+c,PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 21 2017 *)
  • PARI
    is(n)=n%6==1 && isprime(n+16) && isprime(n+64) && isprime(n+256) && isprime(n) \\ Charles R Greathouse IV, Jul 12 2016
  • Perl
    use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256); # Dana Jacobsen, Jul 13 2016

Formula

A049488 INTERSECT A049490 INTERSECT A361483. - R. J. Mathar, Mar 26 2024

A269859 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10, p+2^12 and p+2^14 are all primes.

Original entry on oeis.org

37, 163, 15667, 47287, 120607, 142543, 234067, 263047, 263803, 444607, 607093, 671353, 1447153, 1457857, 1562983, 2162323, 2694157, 2841337, 2979043, 3362143, 3567337, 4890307, 5037433, 5353987, 5772097, 6404773, 6776023, 7717873, 9139453, 9549373, 10550467
Offset: 1

Views

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Keywords

Examples

			The prime 37 is in the sequence, since 37 + 16 = 53, 37 + 64 = 101, 37 + 256 = 293, 37 + 1024 = 1061, 37 + 4096 = 4133 and 37 + 16384 = 16421 are all primes.
The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187, 163 + 4096 = 4259 and 163 + 16384 = 16547 are all primes.

Links

Crossrefs

Subsequence of A269259.
Cf. A269257, A269258.

Programs

  • Magma
    [p: p in PrimesInInterval(2,12000000) | forall{i: i in [16,64,256,1024,4096,16384] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016
  • Mathematica
    m = Map[2^# &, 2 Range[2, 7]]; Select[Prime@ Range[10^6], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)
  • Perl
    use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256,1024,4096,16384); # Dana Jacobsen, Jul 13 2016

A270203 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10, p+2^12, p+2^14 and p + 2^16 are all primes.

Original entry on oeis.org

163, 15667, 234067, 607093, 671353, 1447153, 1457857, 2162323, 5772097, 7717873, 9139453, 9549373, 11170933, 12039883, 13243063, 16442407, 16836163, 17784253, 18116473, 19433863, 21960577, 28209703, 29175283, 32380177, 33890803, 34613287, 34682113
Offset: 1

Views

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Keywords

Examples

			The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187, 163 + 4096 = 4259, 163 + 16384 = 16547 and 163 + 65536 = 65699 are all primes.

Links

Crossrefs

Subsequence of A269859.
Cf. A269257, A269258, A269259.

Programs

  • Magma
    [p: p in PrimesInInterval(2,40000000) | forall{i: i in [16,64,256,1024,4096,16384,65536] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016
  • Mathematica
    m = {2^4, 2^6, 2^8, 2^10, 2^12, 2^14, 2^16}; Select[Prime@ Range[3*10^6], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)
Select[Prime[Range[22*10^5]],AllTrue[#+2^Range[4,16,2],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 12 2018 *)
  • Perl
    use ntheory ":all"; say for sieve_prime_cluster(2,1e8, 16,64,256,1024,4096,16384,65536); # Dana Jacobsen, Jul 13 2016

A275475 Primes p such that p+2^3, p+2^5 and p+2^7 are all primes.

Original entry on oeis.org

11, 29, 71, 149, 491, 599, 701, 1439, 1451, 2339, 3761, 4211, 5399, 5651, 6269, 6701, 7541, 9059, 9311, 9689, 9941, 10859, 11831, 12569, 12791, 13679, 15299, 15551, 16979, 18089, 19301, 19469, 22031, 22541, 23549, 23879, 25229, 25841, 27329, 27791, 28541, 30809
Offset: 1

Views

Author

Debapriyay Mukhopadhyay, Jul 29 2016

Keywords

Examples

			11 is in the sequence because 11+8 = 19, 11+32 = 43 and 11+128 = 139 are all primes.
29 is in the sequence because 29+8 = 37, 29+32 = 61 and 29+128 = 157 are all primes.

Links

Crossrefs

Cf. A269257, A269258, A269259, A269859, A270203.
Cf. A275485 (a subsequence).

Programs

  • Mathematica
    Select[Prime@ Range@ 3450, Function[k, Times @@ Boole@ PrimeQ@ Map[k + 2^# &, {3, 5, 7}] == 1]] (* Michael De Vlieger, Aug 10 2016 *)
Select[Prime[Range[4000]],AllTrue[#+{8,32,128},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 26 2018 *)
  • Perl
    use ntheory ":all"; say for sieve_prime_cluster(2, 1e6, 2**3, 2**5, 2**7); # Dana Jacobsen, Sep 29 2016
Showing 1-5 of 5 results.

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