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 13 results. Next

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

A105610 Numbers k such that both p1=2k+3 and p2=4k+5 are primes.

Original entry on oeis.org

0, 2, 8, 14, 17, 38, 47, 68, 77, 98, 104, 113, 134, 152, 164, 167, 182, 188, 218, 248, 272, 287, 299, 302, 308, 329, 344, 362, 404, 413, 437, 467, 482, 497, 503, 533, 584, 617, 638, 647, 698, 713, 728, 764, 803, 812, 827, 878, 932, 1004, 1013, 1043, 1064, 1067
Offset: 1

Views

Author

Zak Seidov, Apr 15 2005

Keywords

Comments

p1 in A005382, p2 in A005383.

Links

Crossrefs

Cf. A005382, A005383.
Equals A123998 minus 1.

Programs

  • Mathematica
    Select[Range[0,1067], PrimeQ[2#+3]&&PrimeQ[4#+5]&] (* James C. McMahon, Jan 26 2024 *)
  • Python
    from sympy import isprime
print([ k for k in range(0,1068) if isprime(2*k+3) and isprime(4*k+5)])
# Karl-Heinz Hofmann, Jan 27 2024

A124417 a(n) = least k such that 2^i*k+1 is prime for 1<=i<=n.

Original entry on oeis.org

1, 1, 9, 765, 765, 8325, 8325, 7757430, 428547690, 102764221560, 694561346985, 108428872433310, 379041973928475, 34628781572140470, 34628781572140470
Offset: 1

Views

Author

Artur Jasinski, Nov 02 2006

Keywords

Crossrefs

Cf. A005097, A123998, A124041, A124412, A124413, A124414, A124415, A124416.

Programs

  • Mathematica
    k = 1; Do[If[n < 3, inc = 1,If[n == 3, inc = 3, 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, 15}] (* Ray Chandler, Nov 21 2006 *)

Extensions

Edited by Ray Chandler, Nov 21 2006
a(10) from Farideh Firoozbakht, Nov 25 2006
a(11)-a(15) from Giovanni Resta, Apr 24 2019

A124041 Numbers k such that 2*k+1, 4*k+1 and 8*k+1 are primes.

Original entry on oeis.org

9, 39, 165, 219, 249, 309, 414, 534, 639, 765, 1044, 1065, 1089, 1155, 1395, 1509, 1530, 1554, 1590, 1884, 2079, 2115, 2130, 2310, 2319, 2430, 2475, 2709, 2874, 3060, 3105, 3354, 3420, 3684, 3705, 3780, 3819, 4104, 4314, 4554, 4599, 4659, 4869, 5160
Offset: 1

Views

Author

Artur Jasinski, Nov 02 2006

Keywords

Links

Crossrefs

Cf. A005097, A123998, A124412-A124417.

Programs

  • Mathematica
    Select[3*Range[2000], And @@ PrimeQ /@ ({2, 4, 8}*# + 1) &] (* Ray Chandler, Dec 06 2006 *)

A124412 Numbers k such that 2*k+1, 4*k+1, 8*k+1 and 16*k+1 are primes.

Original entry on oeis.org

765, 1065, 1155, 1530, 3105, 3420, 3705, 5160, 6840, 7695, 8325, 9060, 11265, 11505, 12195, 14835, 15390, 15885, 16650, 17655, 20745, 22185, 23205, 27300, 28155, 28995, 30165, 30690, 33300, 33825, 39015, 41715, 42690, 44370, 48465, 49935
Offset: 1

Views

Author

Artur Jasinski, Nov 02 2006

Keywords

Links

Crossrefs

Cf. A005097, A123998, A124041, A124413-A124417.

Programs

  • Mathematica
    Select[15*Range[3500], And @@ PrimeQ /@ ({2, 4, 8, 16}*# + 1) &] (* Ray Chandler, Nov 21 2006 *)

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

A124413 Numbers k such that 2*k+1, 4*k+1, 8*k+1, 16*k+1 and 32*k+1 are primes.

Original entry on oeis.org

765, 3420, 7695, 8325, 16650, 22185, 28995, 33300, 41715, 52935, 72510, 75075, 82950, 99810, 104715, 106425, 115620, 121275, 145635, 159840, 165900, 173070, 188745, 190815, 192795, 222870, 225705, 239400, 240510, 253395, 253890, 256410
Offset: 1

Views

Author

Artur Jasinski, Nov 02 2006

Keywords

Links

Crossrefs

Cf. A005097, A123998, A124041, A124412-A124417.

Programs

  • Mathematica
    Select[15*Range[20000], And @@ PrimeQ /@ ({2, 4, 8, 16, 32}*# + 1) &] (* Ray Chandler, Nov 21 2006 *)
Showing 1-10 of 13 results. Next

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