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.

A230039 Primes p such that 2*p+1 is not prime and 2*p+3 is prime.

Original entry on oeis.org

7, 13, 17, 19, 43, 47, 67, 73, 97, 127, 137, 139, 157, 167, 193, 197, 199, 223, 227, 229, 269, 277, 283, 307, 337, 349, 353, 379, 383, 397, 409, 439, 463, 467, 487, 503, 523, 547, 557, 563, 599, 607, 613, 617, 643, 647, 739, 773, 797, 827, 853, 859, 887, 929
Offset: 1

Views

Author

Vincenzo Librandi, Oct 10 2013

Keywords

Comments

Intersection of A023204 and A053176. - Felix Fröhlich, Jan 14 2017

Examples

			43 is in the sequence because 2*43+1=87 (not prime) and 2*43+3=89 (prime).

Links

Crossrefs

Cf. A005384, A023204, A053176, A126107, A163769, A230117.

Programs

  • Magma
    [p: p in PrimesUpTo(2500)|not IsPrime(2*p+1) and IsPrime(2*p+3)];
  • Mathematica
    Select[Range[10^5],PrimeQ[#]&& !PrimeQ[2#+1]&& PrimeQ[2#+3]&]
  • PARI
    is(n) = ispseudoprime(n) && !ispseudoprime(2*n+1) && ispseudoprime(2*n+3) \\ Felix Fröhlich, Jan 14 2017

A230225 Primes p such that 2*p+1 and 2*p+3 are not prime.

Original entry on oeis.org

31, 37, 59, 61, 71, 79, 101, 103, 107, 109, 149, 151, 163, 181, 211, 241, 257, 263, 271, 311, 313, 317, 331, 347, 367, 373, 389, 401, 421, 433, 449, 457, 461, 479, 499, 521, 541, 569, 571, 577, 587, 601, 619, 631, 661, 673, 677, 691, 701, 709, 727, 733, 751
Offset: 1

Views

Author

Vincenzo Librandi, Oct 12 2013

Keywords

Examples

			31 is in the sequence because 2*31+1=63 and 2*31+3=65 are not prime.

Links

Crossrefs

Cf. A005384, A023204, A053176, A089531, A126107, A163769, A230039, A230117.

Programs

  • Magma
    [p: p in PrimesUpTo(2500)|not IsPrime(2*p+1) and not IsPrime(2*p+3)];
  • Mathematica
    Select[Range[10^3], PrimeQ[#]&&!PrimeQ[2 # + 1]&&!PrimeQ[2 # + 3]&]
Select[Prime[Range[200]],NoneTrue[2#+{1,3},PrimeQ]&] (* Harvey P. Dale, Sep 19 2021 *)

A281022 Single (or isolated or non-twin) primes that are also safe primes.

Original entry on oeis.org

23, 47, 83, 167, 263, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1187, 1283, 1307, 1367, 1439, 1523, 1823, 1907, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903, 2963, 3023, 3203, 3623, 3779, 3803, 3863, 3947, 4007, 4079, 4139, 4283, 4679, 4703, 4919
Offset: 1

Views

Author

Altug Alkan, Jan 13 2017

Keywords

Comments

Primes p such that neither p - 2 nor p + 2 is prime while (p - 1) / 2 is prime.
It is conjectured that there are infinitely many safe primes, but this is still unproved, so it is not known whether this sequence is infinite.

Examples

			23 is a term because 23 - 2 = 21 and 23 + 2 = 25 are composite and (23 - 1) / 2 = 11 is prime.

Links

Crossrefs

Cf. A005385, A007510, A230117.

Programs

  • Mathematica
    Select[Prime[Range[700]],Boole[PrimeQ[{#+2,#-2,(#-1)/2}]]=={0,0,1}&] (* Harvey P. Dale, Aug 14 2023 *)
  • PARI
    lista(nn) = { forprime(p=11, nn, if(!isprime(p+2) && isprime((p-1)/2), print1(p, ", ")));}

Formula

a(n) = 2 * A230117(n+1) + 1, for n > 0.
Showing 1-3 of 3 results.

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

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