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 1-3 of 3 results.

A023261 Primes that remain prime through 2 iterations of function f(x) = 8x + 3.

Original entry on oeis.org

5, 13, 31, 61, 101, 103, 163, 191, 233, 241, 251, 433, 461, 643, 751, 761, 821, 863, 983, 1021, 1153, 1193, 1283, 1291, 1531, 1543, 1861, 2281, 2543, 2903, 2953, 3271, 3373, 3673, 3701, 3733, 3793, 3923, 4003, 4241, 4283, 4751, 5333, 5581, 5711, 5801, 5813
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+3 and 64*p+27 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A005124, A023229. - John Cerkan, Sep 14 2016

Programs

  • Magma
    [n: n in [1..100000] | IsPrime(n) and IsPrime(8*n+3) and IsPrime(64*n+27)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Prime[Range[800]],AllTrue[Rest[NestList[8#+3&,#,2]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2017 *)

Formula

a(n) = 1 or 3 (mod 10) for n > 1. - John Cerkan, Sep 14 2016

A023348 Primes that remain prime through 5 iterations of function f(x) = 8x + 3.

Original entry on oeis.org

774791, 924731, 4593221, 5181641, 9905521, 11523361, 11755831, 12253321, 14078711, 14545331, 14928791, 18523361, 18686531, 24169001, 25614361, 26221051, 26834461, 30970201, 33446521, 40051021, 42888191, 43703201, 47528561, 48653951
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+3, 64*p+27, 512*p+219, 4096*p+1755 and 32768*p+14043 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A005124, A023229, A023261, A023292, and A023320.

Programs

  • Magma
    [n: n in [1..19000000] | IsPrime(n) and IsPrime(8*n+3) and IsPrime(64*n+27) and IsPrime(512*n+219) and IsPrime(4096*n+1755) and IsPrime(32768*n+14043)] // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    n5Q[n_]:=And@@PrimeQ/@NestList[8#+3&,n,5]; Select[Prime[Range[ 3000000]], n5Q] (* Harvey P. Dale, Sep 03 2013 *)

Formula

a(n) == 31 (mod 70). - John Cerkan, Nov 04 2016

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
Showing 1-3 of 3 results.

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

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