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.

A089193 Odd numbers n such that 2*n-7 is a prime of the form 4*k+3.

Original entry on oeis.org

5, 7, 9, 13, 15, 19, 25, 27, 33, 37, 39, 43, 45, 55, 57, 67, 69, 73, 79, 85, 87, 93, 99, 103, 109, 115, 117, 123, 129, 135, 139, 145, 157, 159, 169, 177, 183, 187, 193, 195, 213, 219, 223, 225, 235, 237, 243, 247, 249, 253, 255, 265, 277, 285, 289, 297, 303
Offset: 1

Views

Author

Giovanni Teofilatto, Dec 08 2003

Keywords

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997.

Links

Crossrefs

Cf. A002145, A087915.

Programs

  • Mathematica
    tn7Q[n_]:=Module[{c=2n-7},PrimeQ[c]&&Divisible[c-3,4]]; Select[Range[ 5,301,2],tn7Q] (* Harvey P. Dale, May 18 2021 *)

Formula

a(n) = A087915(n) + 5.

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 09 2011
Corrected and extended by Harvey P. Dale, May 18 2021

A090670 Odd numbers k such that 2*k-3 is a prime of the form 4*j+3.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 23, 25, 31, 35, 37, 41, 43, 53, 55, 65, 67, 71, 77, 83, 85, 91, 97, 101, 107, 113, 115, 121, 127, 133, 137, 143, 155, 157, 167, 175, 181, 185, 191, 193, 211, 217, 221, 223, 233, 235, 241, 245, 247, 251, 253, 263, 275, 283, 287, 295, 301, 305
Offset: 1

Views

Author

Giovanni Teofilatto, Dec 17 2003

Keywords

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

Links

Crossrefs

Cf. A087915, A002145.
Cf. A050415 (primes of the form 2^k-3).

Programs

  • Mathematica
    okQ[n_]:=Module[{x=2n-3},PrimeQ[x]&&IntegerQ[(x-3)/4]]; Select[Range[1,315,2],okQ]  (* Harvey P. Dale, Jan 12 2011 *)

Formula

a(n) = A087915(n)+3.

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Dec 13 2011

A090658 Numbers n such that n-1 is a prime of the form 4k+3.

Original entry on oeis.org

4, 8, 12, 20, 24, 32, 44, 48, 60, 68, 72, 80, 84, 104, 108, 128, 132, 140, 152, 164, 168, 180, 192, 200, 212, 224, 228, 240, 252, 264, 272, 284, 308, 312, 332, 348, 360, 368, 380, 384, 420, 432, 440, 444, 464, 468, 480, 488, 492, 500, 504, 524, 548, 564, 572
Offset: 1

Views

Author

Giovanni Teofilatto, Dec 14 2003

Keywords

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997

Links

Crossrefs

Cf. A002145, A087915, A089193, A089257.

Programs

  • Mathematica
    okQ[n_]:=Module[{x=n-1},PrimeQ[x]&&IntegerQ[(x-3)/4]];Select[Range[1,1000,1],okQ] (* Vincenzo Librandi, Dec 13 2011 *)
Select[4*Range[0,200]+3,PrimeQ]+1 (* Harvey P. Dale, Sep 25 2017 *)

Formula

a(n) = A087915(n)+A089257(n), A089193(n)+A089257(n)-5.

Extensions

Corrected and extended by T. D. Noe, Oct 25 2006

A089217 n-2 is a prime of the form 4*k+3.

Original entry on oeis.org

5, 9, 13, 21, 25, 33, 45, 49, 61, 69, 73, 81, 85, 105, 109, 129, 133, 141, 153, 165, 169, 181, 193, 201, 213, 225, 229, 241, 253, 265, 273, 285, 309, 313, 333, 349, 361, 369, 381, 385, 421, 433, 441, 445, 465, 469, 481, 489, 493, 501, 505, 525, 549, 565, 573
Offset: 1

Views

Author

Giovanni Teofilatto, Dec 10 2003

Keywords

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997.

Crossrefs

Cf. A087915, A089193.

Programs

  • Mathematica
    Select[4*Range[0,200]+3,PrimeQ]+2 (* Harvey P. Dale, Jun 04 2017 *)

Formula

a(n) = A087915(n)+ A089193(n)

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 09 2011
Corrected and extended by Harvey P. Dale, Jun 04 2017

A141544 Odd numbers k such that 2k+5 is a prime.

Original entry on oeis.org

1, 3, 7, 9, 13, 19, 21, 27, 31, 33, 37, 39, 49, 51, 61, 63, 67, 73, 79, 81, 87, 93, 97, 103, 109, 111, 117, 123, 129, 133, 139, 151, 153, 163, 171, 177, 181, 187, 189, 207, 213, 217, 219, 229, 231, 237, 241, 243, 247, 249, 259, 271, 279, 283, 291, 297, 301, 307
Offset: 1

Views

Author

Giovanni Teofilatto, Aug 16 2008

Keywords

Comments

Superset of A107771. The corresponding primes are given by deleting the first entry in A002145. - R. J. Mathar, Aug 18 2008

Crossrefs

Cf. A002145, A020498, A087915, A089038, A090670, A107771.

Programs

  • Maple
    a:=proc(n) if isprime(2*n+5) then n end if end proc: seq(a(2*n-1), n=1..170); # Emeric Deutsch, Aug 17 2008
  • Mathematica
    Select[Range[1,307,2],PrimeQ[2#+5]&] (* James C. McMahon, Jul 26 2025 *)

Formula

A089038 INTERSECT A005408. - R. J. Mathar, Aug 18 2008
a(n) = A087915(n+1) - 1 = A090670(n+1) - 4. - Giovanni Teofilatto, Sep 07 2008

Extensions

Extended by Emeric Deutsch, Aug 17 2008 and R. J. Mathar, Aug 18 2008
Showing 1-5 of 5 results.

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