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 1-10 of 11 results. Next

A123248 Largest prime factor in A071576 starting from 4th position.

Original entry on oeis.org

11, 19, 11, 37, 37, 13109, 1607621, 70381, 1801273, 1483, 52489012879
Offset: 1

Views

Author

Artur Jasinski, Nov 06 2006

Keywords

Crossrefs

Cf. A071576.

Formula

a(n) = A006530(A071576(n+3)). - Amiram Eldar, Mar 23 2020

Extensions

a(11) calculated from the data at A071576 by Amiram Eldar, Mar 23 2020

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

A124516 a(n) = least k such that 2^i*k-1 is prime for 1<=i<=n.

Original entry on oeis.org

2, 2, 3, 3, 45, 45, 561330, 9549960, 42932385, 13044904290, 277344139215, 277344139215, 2045466215756535
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Crossrefs

Cf. A006254, A124485, A124493, A124494, A124017, A125113, A124514, A124515.
Cf. A071576, A101994, A101320.

Programs

  • Mathematica
    k = 1; Do[If[n < 5, inc = 1, inc = 15];If[Mod[k, inc] > 0, k = k + inc - Mod[k, inc]];While[Nand @@ PrimeQ[Table[2^j, {j, n}]*k - 1], k += inc]; Print[k], {n, 1, 10}] (* Ray Chandler *)

Extensions

Definition corrected and a(10) calculated by Farideh Firoozbakht, Nov 24 2006
a(11)-a(13) from Giovanni Resta, Apr 22 2019

A124492 a(n) = least k such that 2*i*k - 1 is prime for 1 <= i <= n.

Original entry on oeis.org

2, 2, 2, 3, 3, 77385, 1447110, 1447110, 203937090, 107290072890, 4724240531010, 123618251967210, 1272603355923900, 9089306184994125090
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Crossrefs

Cf. A006254, A124485-A124491, A071576.

Programs

  • Mathematica
    a[n_] := Block[{k = If[n < 6, 1, 5], s}, s = k; While[! AllTrue[k  2 Range[n] - 1, PrimeQ], k += s]; k]; Array[a, 8] (* Giovanni Resta, Apr 01 2017 *)

Extensions

Corrected and extended by Don Reble, Nov 05 2006
a(12)-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

A124411 Numbers k such that 2k+1, 4k+1, 6k+1, 8k+1, 10k+1 and 12k+1 are primes.

Original entry on oeis.org

12705, 13020, 105525, 256410, 966840, 1707510, 1944495, 2310000, 2478630, 3132675, 3836070, 3976770, 4112430, 4532325, 5499585, 5920005, 6610485, 7390845, 8552250, 10739505, 11120340, 12231450, 12338130, 13243230, 16467255
Offset: 1

Views

Author

Artur Jasinski, Oct 31 2006

Keywords

Links

Crossrefs

Cf. A005097, A005098, A024899, A005123, A024912, A110801, A123998, A124408, A124409, A124410, A071576.

Programs

  • Mathematica
    Select[Range[10^7], And @@ PrimeQ /@ ({2, 4, 6, 8, 10, 12}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)
  • PARI
    is(k) = sum(j = 1, 6, isprime(2*j*k+1)) == 6; \\ Jinyuan Wang, Aug 04 2019

Extensions

Extended by Ray Chandler, Nov 20 2006

A244433 a(n) is the smallest number m such that 2im+1 is composite for all i, 0

Original entry on oeis.org

4, 12, 19, 19, 59, 92, 159, 159, 159, 227, 227, 256, 256, 256, 514, 514, 706, 706, 706, 706, 706, 706, 706, 1466, 1466, 1466, 1466, 1466, 1466, 5207, 5207, 5207, 5207, 5207, 5207, 5207, 5207, 5207, 5207, 5207, 5207, 21209, 21209, 21209, 21209, 21209, 21209, 21209, 21209, 21209, 21209, 21209, 21209, 62809, 62809, 62809, 86914, 86914, 86914, 152351
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 18 2014

Keywords

Comments

a(3)=a(4)=19, a(7)=a(8)=a(9)=159, ..., a(74)=a(75)=...=a(82)=424783, ... . A244434 gives numbers n such that a(n) does not belong to the set {a(n-1),a(n+1)}.

Examples

			a(3)=19 because all the three numbers 2*1*19+1=39, 2*2*19+1=77 & 2*3*19+1=115 are composite and 19 is the smallest such number.

Crossrefs

Cf. A071576, A244434, A244435.

A164325 a(n) is the smallest number m such that (2k-1)m+1 is prime for all 0

Original entry on oeis.org

1, 2, 2, 6, 1170, 64590, 25153800, 25153800, 4747505070, 207187349040, 6703860240000, 26997529639080, 1760354281625940, 1760354281625940, 10718654377787155800
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 15 2009

Keywords

Crossrefs

Cf. A088250, A071576, A164326, A088251, A088651, A125838, A125839, A088252.

Extensions

a(5) corrected by Zak Seidov, Sep 16 2009
a(10) and a(11) from Zak Seidov, Sep 17 2009
a(12)=26997529639080 from Zak Seidov, Sep 25 2009
a(13)-a(15) from Giovanni Resta, Apr 01 2017
Showing 1-10 of 11 results. Next

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

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