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.

A123998 Numbers k such that 2k+1 and 4k+1 are primes.

Original entry on oeis.org

1, 3, 9, 15, 18, 39, 48, 69, 78, 99, 105, 114, 135, 153, 165, 168, 183, 189, 219, 249, 273, 288, 300, 303, 309, 330, 345, 363, 405, 414, 438, 468, 483, 498, 504, 534, 585, 618, 639, 648, 699, 714, 729, 765, 804, 813, 828, 879, 933, 1005, 1014, 1044, 1065, 1068
Offset: 1

Views

Author

Artur Jasinski, Oct 31 2006

Keywords

Comments

Note that if n == 1 (mod 3) then 2n+1 is not prime (except n=1); and if n == 2 (mod 3) then 4n+1 is not prime. Therefore n must be a multiple of 3, except for n=1. - Max Alekseyev, Nov 02 2006

Links

Crossrefs

Cf. A005097, A005098, A124408, A124409, A124410, A124411, A071576.

Programs

  • Magma
    [n: n in [0..1100] |IsPrime(2*n+1) and IsPrime(4*n+1)]; // Vincenzo Librandi, Apr 17 2013
  • Mathematica
    Select[Range[1100], And @@ PrimeQ /@ ({2, 4}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)
  • PARI
    is(k) = isprime(2*k+1) && isprime(4*k+1); \\ Jinyuan Wang, Aug 04 2019

Extensions

Extended by Ray Chandler, Nov 20 2006

A071576 a(n) = least k such that 2ik + 1 is prime for all 1 <= i <= n.

Original entry on oeis.org

1, 1, 1, 165, 5415, 12705, 256410, 256410, 6480303060, 217245863835, 946622690475, 35511547806735, 439116128090640, 5714676453270219435
Offset: 1

Views

Author

Benoit Cloitre, May 31 2002

Keywords

Crossrefs

Cf. A088250, A124516, A124522, A124522, A063983.
Cf. A005097, A123998, A124408-A124411.

Programs

  • Mathematica
    k = 1; Do[ While[p = Table[2*i*k + 1, {i, 1, n}]; Union[ PrimeQ[p]] != {True}, k++ ]; Print[k], {n, 1, 15}] (* Robert G. Wilson v *)
  • PARI
    for(n=1,6,s=1; while(sum(i=1,n,isprime(2*s*i+1))

Extensions

Extended by Robert G. Wilson v, Jun 06 2002
a(9) from Ryan Propper, Jun 20 2005
a(10)-a(13) from Don Reble, Nov 05 2006
a(14) from Giovanni Resta, Apr 01 2017

A124408 Numbers k such that 2k+1, 4k+1 and 6k+1 are primes.

Original entry on oeis.org

1, 3, 18, 105, 135, 153, 165, 168, 300, 363, 585, 618, 648, 765, 828, 1110, 1140, 1278, 1518, 1530, 1533, 2130, 2223, 2400, 2475, 2613, 2790, 2925, 3075, 3180, 3345, 3420, 3483, 3810, 3840, 3843, 3933, 4008, 4083, 4095, 4143, 4260, 4263, 4323, 4470, 4545
Offset: 1

Views

Author

Artur Jasinski, Oct 31 2006

Keywords

Links

Crossrefs

Cf. A005097, A005098, A024899, A123998, A124409, A124410, A124411, A071576.

Programs

  • Mathematica
    Select[Range[4600], And @@ PrimeQ /@ ({2, 4, 6}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)
  • PARI
    is(k) = sum(j = 1, 3, isprime(2*j*k+1)) == 3; \\ Jinyuan Wang, Aug 04 2019

A124409 Numbers k such that 2k+1, 4k+1, 6k+1 and 8k+1 are primes.

Original entry on oeis.org

165, 765, 1530, 2130, 2475, 3420, 5415, 7695, 9060, 11505, 12705, 13020, 15885, 16650, 20055, 20745, 22530, 24915, 26940, 29670, 32925, 35070, 36885, 39270, 44370, 47730, 48465, 54735, 55860, 56310, 58860, 65655, 66600, 67365, 67650
Offset: 1

Views

Author

Artur Jasinski, Oct 31 2006

Keywords

Links

Crossrefs

Cf. A005097, A005098, A024899, A005123, A123998, A124408, A124410, A124411, A071576.

Programs

  • Mathematica
    Select[Range[68000], And @@ PrimeQ /@ ({2, 4, 6, 8}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)
  • PARI
    is(k) = sum(j = 1, 4, isprime(2*j*k+1)) == 4; \\ Jinyuan Wang, Aug 04 2019

A124410 Numbers k such that 2k+1, 4k+1, 6k+1, 8k+1 and 10k+1 are primes.

Original entry on oeis.org

5415, 12705, 13020, 44370, 82950, 98280, 105525, 112200, 115140, 123855, 134250, 134460, 187740, 188745, 210165, 225705, 247170, 256410, 296310, 302085, 367875, 375645, 382890, 399585, 404040, 476340, 487830, 526845, 532095, 566430, 578085
Offset: 1

Views

Author

Artur Jasinski, Oct 31 2006

Keywords

Links

Crossrefs

Cf. A005097, A005098, A024899, A005123, A024912, A123998, A124408, A124409, A124411, A071576.

Programs

  • Mathematica
    Select[Range[600000], And @@ PrimeQ /@ ({2, 4, 6, 8, 10}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)
  • PARI
    is(k) = sum(j = 1, 5, isprime(2*j*k+1)) == 5; \\ Jinyuan Wang, Aug 04 2019
Showing 1-5 of 5 results.

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