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 1-7 of 7 results.

A023262 Primes that remain prime through 2 iterations of the function f(x) = 8*x + 5.

Original entry on oeis.org

13, 43, 103, 139, 199, 349, 397, 577, 727, 733, 829, 967, 1039, 1303, 1567, 1597, 1753, 2131, 2161, 2311, 2707, 2719, 2857, 3109, 3319, 3613, 3673, 3697, 3853, 4051, 4129, 4201, 4297, 4441, 4507, 4513, 4639, 4663, 4789, 5503, 5701, 5743, 5857, 5953, 6121
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+5 and 64*p+45 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023230, A105133.

Programs

  • Magma
    [n: n in [1..100000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45)] // Vincenzo Librandi, Aug 04 2010

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 16 2016

A023293 Primes that remain prime through 3 iterations of function f(x) = 8x + 5.

Original entry on oeis.org

43, 103, 199, 1039, 1303, 2311, 2857, 3673, 4513, 4663, 5743, 5953, 8431, 9721, 12391, 14143, 14533, 17599, 18457, 19507, 21211, 23719, 24169, 25621, 28663, 29023, 31963, 33409, 35311, 36979, 37423, 40867, 40939, 43891, 44371, 44983, 45841, 46747, 46807
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+5, 64*p+45 and 512*p+365 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023230, A023262, and A105133.

Programs

  • Magma
    [n: n in [1..450000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45) and IsPrime(512*n+365)]; // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Prime[Range[5000]],AllTrue[Rest[NestList[8#+5&,#,3]],PrimeQ]&] (* Harvey P. Dale, Sep 19 2022 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 23 2016

A023321 Primes that remain prime through 4 iterations of function f(x) = 8x + 5.

Original entry on oeis.org

8431, 9721, 24169, 35311, 63577, 74203, 109471, 109891, 140269, 174613, 176599, 182857, 210187, 241561, 270553, 274837, 274909, 276517, 281557, 324763, 326737, 383659, 464089, 474127, 489109, 498403, 540781, 563587, 576943, 582949, 633253
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+5, 64*p+45, 512*p+365 and 4096*p+2925 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023230, A023262, A023293, and A105133.

Programs

  • Magma
    [n: n in [1..5000000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45) and IsPrime(512*n+365) and IsPrime(4096*n+2925)] // Vincenzo Librandi, Aug 04 2010

Formula

a(n) == 19 or 31 (mod 42). - John Cerkan, Oct 08 2016

A023349 Primes that remain prime through 5 iterations of function f(x) = 8x + 5.

Original entry on oeis.org

109891, 324763, 852367, 3371527, 3557797, 4448701, 4471549, 5304661, 5616679, 5688919, 5727349, 7766659, 8028109, 8554999, 9034723, 10867099, 11146987, 12396487, 12926401, 14186611, 18274513, 19251517, 20882713, 21810493, 23953921
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+5, 64*p+45, 512*p+365, 4096*p+2925 and 32768*p+23405 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A023230, A023262, A023293, A023321, and A105133.

Programs

  • Magma
    [n: n in [1..19000000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45) and IsPrime(512*n+365) and IsPrime(4096*n+2925) and IsPrime(32768*n+23405)] // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    p5Q[n_]:=And@@PrimeQ/@NestList[8#+5&,n,5]; Parallelize[Select[Prime[Range[1510000]],p5Q]] (* Harvey P. Dale, Feb 22 2011 *)

Formula

a(n) == 19 (mod 42). - John Cerkan, Nov 06 2016

A164569 Primes p such that 11*p+8 are prime numbers.

Original entry on oeis.org

3, 13, 31, 73, 79, 151, 163, 181, 193, 241, 283, 349, 373, 379, 409, 421, 463, 601, 631, 673, 751, 769, 811, 829, 853, 883, 991, 1021, 1039, 1063, 1171, 1201, 1303, 1381, 1423, 1429, 1453, 1459, 1471, 1543, 1549, 1579, 1609, 1621, 1663, 1669, 1789, 1801
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Apart from the first term, a(n) = 1 (mod 6).

Examples

			11*3+8=41, ..

Crossrefs

Cf. A023212, A023217, A023224, A023230, A023239

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[11*p+8],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[500]],PrimeQ[11#+8]&] (* Harvey P. Dale, Jul 17 2011 *)

Extensions

Comment from Charles R Greathouse IV, Oct 12 2009

A164570 Primes p such that 8*p-3 and 8*p+3 are also prime numbers.

Original entry on oeis.org

2, 5, 7, 13, 47, 103, 107, 127, 163, 233, 293, 337, 383, 433, 443, 467, 503, 673, 677, 733, 797, 877, 1087, 1093, 1153, 1217, 1223, 1307, 1637, 1933, 2053, 2087, 2137, 2423, 2477, 2543, 2633, 2687, 2857, 2917, 3163, 3373, 3407, 3467, 3767, 3793, 3877
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Subsequence of A023229. [R. J. Mathar, Aug 26 2009]
Primes of the form A087695(k)/8. [R. J. Mathar, Aug 26 2009]

Examples

			For p=2, 8*2-3=13 and 8*2+3=19 are prime numbers, which adds p=2 to the sequence
For p=5, 8*5-3=37 and 8*5+3=43 are prime numbers, which adds p=5 to the sequence.

Links

Crossrefs

Cf. A023212, A023217, A023224, A023230, A023239, A060212, A106015, A124098, A125272, A127430, A153768, A164566, A164567, A164568, A164569.

Programs

  • Magma
    [p: p in PrimesUpTo(3000) | IsPrime(8*p-3) and IsPrime(8*p+3)]; // Vincenzo Librandi, Apr 09 2013
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[8*p-3]&&PrimeQ[8*p+3],AppendTo[lst,p]], {n,7!}];lst
Select[Prime[Range[1000]], And@@PrimeQ/@{8 # + 3, 8 # - 3}&] (* Vincenzo Librandi, Apr 09 2013 *)
Select[Prime[Range[1000]],AllTrue[8#+{3,-3},PrimeQ]&] (* Harvey P. Dale, May 05 2023 *)

Extensions

Comments turned into examples by R. J. Mathar, Aug 26 2009

A106080 Primes p such that 5*p+8 and 8*p+5 are primes.

Original entry on oeis.org

3, 7, 13, 19, 43, 103, 127, 211, 223, 241, 283, 349, 397, 421, 439, 727, 733, 787, 829, 853, 883, 1597, 1723, 1741, 1777, 2017, 2131, 2287, 2371, 2383, 2521, 2593, 2833, 2857, 3163, 3181, 3253, 3319, 3571, 3583, 3697, 3853, 3919, 3967, 4003, 4021, 4201
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Programs

  • Magma
    [p: p in PrimesUpTo(10000)| IsPrime(5*p+8) and IsPrime(8*p+5)] // Vincenzo Librandi, Nov 13 2010
  • Mathematica
    Select[Prime[Range[220]], PrimeQ[8#+5]&&PrimeQ[5#+8]&]

Formula

A023220 INTERSECT A023230. - R. J. Mathar, Aug 06 2009

Extensions

More terms from Vincenzo Librandi, Apr 01 2010
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.