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.

A107020 Primes p such that 2p+1, 4p+3, 6p+5 are all primes.

Original entry on oeis.org

2, 11, 41, 1901, 2459, 5081, 5849, 6131, 6449, 8969, 9221, 10691, 12119, 13229, 14009, 14321, 14669, 15161, 18461, 19709, 20411, 21179, 22271, 23099, 24551, 25601, 30389, 37991, 39419, 41381, 43691, 44699, 52289, 55631, 56081, 58979
Offset: 1

Views

Author

Zak Seidov, May 09 2005

Keywords

Links

Crossrefs

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107020: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).
Cf. A005384, A007700, A107021, A107022, A107023, A107024.

Programs

  • Magma
    [p: p in PrimesUpTo(1000000)| IsPrime(2*p+1) and IsPrime(4*p+3) and IsPrime(6*p+5) ]; // Vincenzo Librandi, Nov 13 2010
  • Mathematica
    Select[Range[60000],AllTrue[{#,2#+1,4#+3,6#+5},PrimeQ]&] (* James C. McMahon, Feb 09 2024 *)

Extensions

More terms from Vincenzo Librandi, Apr 01 2010

A107022 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 are all primes.

Original entry on oeis.org

2, 6449, 210209, 244589, 528509, 810539, 968729, 985109, 1316699, 1551899, 1743419, 2832629, 4094999, 4328459, 5608409, 6036869, 7077419, 7939829, 8176979, 8673569, 8789279, 9080189, 9797279, 10122419, 10309889, 10487969
Offset: 1

Views

Author

Zak Seidov, May 09 2005

Keywords

Links

Crossrefs

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107021: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime;A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).
Cf. A005384, A007700, A107020, A107021, A107023, A107024.

Programs

  • Magma
    [p: p in PrimesUpTo(100000000)| IsPrime(2*p+1) and IsPrime(4*p+3) and IsPrime(6*p+5) and IsPrime(8*p+7)and IsPrime(10*p+9)]; // Vincenzo Librandi, Nov 13 2010
  • Mathematica
    Select[Prime[Range[700000]],And@@PrimeQ[{2#+1,4#+3,6#+5,8#+7,10#+9}]&] (* Harvey P. Dale, Jun 19 2013 *)
Select[Prime[Range[700000]],AllTrue[Table[2n #+2n-1,{n,5}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 22 2018 *)

Extensions

More terms from Vincenzo Librandi, Apr 01 2010

A107023 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 are all primes.

Original entry on oeis.org

4094999, 9080189, 10957169, 11148899, 15917579, 19422059, 37267229, 37622339, 58680929, 63196349, 64595369, 66383519, 108463739, 177109379, 186977699, 189997079, 196068179, 228875849, 251891639, 261703889, 271031669, 310143959
Offset: 1

Views

Author

Zak Seidov, May 09 2005, Mar 08 2007

Keywords

Examples

			a(1) = p = 4094999 is a term because numbers i*p+(i-1), i=2(2)12 8189999,16379999,24569999,32759999,40949999,49139999 are all primes.

Links

Crossrefs

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107021: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime;A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).
Cf. A005384, A007700, A107020, A107021, A107022, A107024.

Programs

  • Mathematica
    s={};Do[p=Prime[i]; If[Union[PrimeQ[Table[i*p+(i-1),{i,2,12,2}]]]=={True},AppendTo[s,p]],{i,289435,1236230}];s
With[{t=Table[2n #+(2n-1),{n,6}]},Select[Prime[ Range[ 168*10^5]], AllTrue[ t,PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 14 2018 *)

A107024 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 are all primes.

Original entry on oeis.org

4094999, 9080189, 63196349, 66383519, 177109379, 196068179, 310143959, 389825729, 528083219, 909696059, 937924259, 1080610439, 1318820159, 1342772969, 1824166469, 1921977329
Offset: 1

Views

Author

Zak Seidov, May 09 2005

Keywords

Links

Crossrefs

Cf. A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107021: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime; A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).
Cf. A005384, A007700, A107020-A107023.

A329551 Primes p such that 4*p+3, 6*p+5 and 8*p+7 are all primes.

Original entry on oeis.org

2, 59, 107, 227, 389, 587, 839, 977, 1217, 1259, 1319, 2957, 3947, 4889, 5189, 5519, 6449, 7949, 8039, 8297, 8609, 9467, 11279, 11399, 12119, 13397, 14627, 14969, 15497, 15647, 19709, 22229, 22907, 25847, 27437, 28619, 29759, 30389, 32609, 34877, 36497, 37277, 39857, 40289, 42569, 45779, 46889
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, Nov 16 2019

Keywords

Comments

All terms but the first == 17 or 29 (mod 30).
Thus the least possible difference between successive terms is 12.
The first terms p such that p+12 is also a term are 3518687, 5412257, 9447017, 10454177, 45093887, 58628777, 94327967.

Examples

			a(4)=227 is a member because 227, 4 * 227 + 3 = 911, 6 * 227 + 5 = 1367, and 8 * 227 + 7 = 1823 are all primes.

Links

Crossrefs

Contains A107021.

Programs

  • Magma
    [p:p in PrimesUpTo(50000)|forall{m: m in [-2*p-2,0,2*p+2]| IsPrime(6*p+5+m)}]; // Marius A. Burtea, Nov 17 2019
  • Maple
    filter:= p -> isprime(p) and isprime(4*p+3) and isprime(6*p+5) and isprime(8*p+7):
select(filter, [2, seq(i,i=5..100000, 6)]);
  • Mathematica
    Select[Prime[Range[5000]],AllTrue[{4#+3,6#+5,8#+7},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 08 2021 *)
Showing 1-5 of 5 results.

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