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.

Previous Showing 11-20 of 27 results. Next

A125966 Numbers k for which k^10+k^9-1 is prime.

Original entry on oeis.org

4, 10, 13, 15, 16, 31, 36, 59, 65, 73, 90, 91, 95, 104, 105, 118, 119, 123, 125, 164, 185, 189, 199, 216, 230, 246, 254, 279, 295, 296, 298, 300, 331, 338, 344, 356, 361, 374, 384, 409, 413, 431, 435, 441, 485, 501, 519, 521, 525, 583, 599, 609, 619, 625, 636
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125973.

Programs

  • Mathematica
    Do[If[PrimeQ[x^10 + x^9 - 1], Print[x]], {x, 1, 400}]
  • PARI
    is(n)=isprime(n^10+n^9-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020

A125972 Numbers k for which k^15+k^14-1 is prime.

Original entry on oeis.org

7, 26, 42, 49, 116, 130, 149, 159, 190, 277, 289, 295, 296, 310, 330, 334, 365, 386, 389, 406, 411, 419, 471, 492, 505, 541, 590, 602, 632, 687, 690, 704, 727, 770, 771, 804, 826, 844, 872, 882, 929, 949, 961, 1017, 1082, 1091, 1135, 1157, 1160, 1196, 1232, 1237
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125973.

Programs

  • Mathematica
    Do[If[PrimeQ[x^15 + x^14 - 1], Print[x]], {x, 1, 600}]
  • PARI
    is(n)=isprime(n^15+n^14-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020

A154667 Averages of twin prime pairs such that p1 * p2 + AverageTwinPrime is prime.

Original entry on oeis.org

4, 6, 30, 60, 138, 180, 240, 420, 618, 1050, 1608, 1698, 1788, 2268, 2310, 2730, 3258, 3390, 3528, 3768, 4158, 4218, 4338, 4800, 5640, 5868, 6660, 6690, 6870, 6960, 7488, 7548, 7590, 8538, 8628, 8970, 9630, 9858, 9930, 10458, 11118, 11970, 12540, 13338
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Keywords

Examples

			3*5 + 4 = 19.
5*7 + 6 = 41.

Links

Crossrefs

Cf. A154666.
A014574 INTERSECT A045546. - R. J. Mathar, May 31 2010

Programs

  • Magma
    [p+1:p in PrimesUpTo(14000)|IsPrime(p+2) and IsPrime(p*(p+2)+p+1)]; // Marius A. Burtea, Dec 21 2019
  • Mathematica
    lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],If[PrimeQ[(n-1)*(n+1)+n],AppendTo[lst,n]]],{n,8!}];lst

A230515 Numbers n such that n*(n+1)-1 is a Sophie Germain prime.

Original entry on oeis.org

2, 3, 5, 6, 9, 11, 15, 20, 38, 39, 45, 48, 50, 54, 59, 93, 126, 131, 144, 149, 153, 174, 176, 218, 231, 236, 240, 246, 248, 263, 285, 306, 309, 330, 335, 374, 380, 395, 396, 401, 419, 423, 449, 455, 468, 471, 474, 495, 501, 506, 549, 551, 560, 588
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 21 2013

Keywords

Comments

This sequence is interesting because of the conjecture associated with A230514.

Examples

			a(1) = 2 since 2*3 - 1 = 5 is a Sophie Germain prime.
a(2) = 3 since 3*4 - 1 = 11 is a Sophie Germain prime.
a(3) = 5 since 5*6 - 1 = 29 is a Sophie Germain prime but 4*5 - 1 = 19 is not.

Links

Crossrefs

Cf. A000040, A005384, A230514.
Subsequence of A045546.

Programs

  • Magma
    [n: n in [1..600] | IsPrime(n*(n+1)-1) and IsPrime(2*n*(n+1)-1)]; // Bruno Berselli, Oct 22 2013
  • Mathematica
    q[n_]:=PrimeQ[n(n+1)-1]&&PrimeQ[2n(n+1)-1]
m=0
Do[If[q[n],m=m+1;Print[m," ",n]],{n,1,506}]
Select[Range[600],AllTrue[{#^2+#-1,2#^2+2#-1},PrimeQ]&] (* Harvey P. Dale, Dec 02 2021 *)

A236056 Numbers k such that k^2 +- k +- 1 is prime for all four possibilities.

Original entry on oeis.org

3, 6, 21, 456, 1365, 2205, 2451, 2730, 8541, 18486, 32199, 32319, 32781, 45864, 61215, 72555, 72561, 82146, 83259, 86604, 91371, 95199, 125334, 149331, 176889, 182910, 185535, 210846, 225666, 226254, 288420, 343161, 350091, 403941, 411501, 510399, 567204
Offset: 1

Views

Author

Derek Orr, Jan 18 2014

Keywords

Comments

The only prime in this sequence is a(1) = 3.

Examples

			1365^2 + 1365 + 1 = 1864591,
1365^2 + 1365 - 1 = 1864589,
1365^2 - 1365 + 1 = 1861861, and
1365^2 - 1365 - 1 = 1861859 are all prime, so 1365 is a term of this sequence.

Crossrefs

Numbers in the intersection of A002384, A045546, A055494, and A002328.
Numbers in the intersection of A131530 and A088485.

Programs

  • Maple
    q:= k-> andmap(isprime, [seq(seq(k^2+i+j, j=[k, -k]), i=[1, -1])]):
select(q, [3*t$t=1..200000])[];  # Alois P. Heinz, Feb 25 2020
  • Mathematica
    Select[Range[568000],AllTrue[Flatten[{#^2+#+{1,-1},#^2-#+{1,-1}},1],PrimeQ]&] (* Harvey P. Dale, Jul 31 2022 *)
  • Python
    import sympy
from sympy import isprime
{print(p) for p in range(10**6) if isprime(p**2+p+1) and isprime(p**2-p+1) and isprime(p**2+p-1) and isprime(p**2-p-1)}

A125967 Numbers n for which n^9+n^8-1 is prime.

Original entry on oeis.org

14, 21, 27, 42, 51, 53, 69, 78, 90, 104, 111, 128, 137, 149, 156, 159, 190, 219, 231, 247, 254, 289, 315, 322, 330, 331, 336, 344, 354, 397, 414, 432, 442, 449, 452, 456, 469, 473, 491, 511, 541, 551, 566, 581, 614, 621, 648, 683, 687, 692, 698, 699, 702, 707, 740, 771, 772, 775, 813, 820, 832
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125973.

Programs

  • Maple
    filter:= k -> isprime(k^9+k^8-1):
select(filter, [$1..1000]); # Robert Israel, Oct 07 2019
  • Mathematica
    Do[If[PrimeQ[x^9 + x^8 - 1], Print[x]], {x, 1, 400}]
  • PARI
    is(n)=isprime(n^9+n^8-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Robert Israel, Oct 07 2019

A125968 Numbers k for which k^11+k^10-1 is prime.

Original entry on oeis.org

7, 9, 20, 40, 49, 56, 59, 74, 77, 114, 125, 140, 146, 170, 180, 192, 214, 295, 301, 339, 344, 349, 387, 397, 416, 431, 435, 447, 455, 462, 482, 499, 506, 525, 564, 566, 582, 600, 611, 625, 634, 642, 676, 679, 691, 699, 700, 716, 719, 740, 769, 780, 792, 807, 819
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125973.

Programs

  • Mathematica
    Do[If[PrimeQ[x^11 + x^10 - 1], Print[x]], {x, 1, 400}]
  • PARI
    is(n)=isprime(n^11+n^10-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020

A125969 Numbers k for which k^12+k^11-1 is prime.

Original entry on oeis.org

2, 5, 9, 10, 11, 12, 13, 24, 30, 31, 48, 49, 60, 61, 71, 85, 96, 104, 131, 132, 147, 167, 175, 185, 191, 198, 204, 218, 226, 242, 269, 305, 323, 340, 385, 386, 406, 437, 471, 500, 526, 534, 549, 570, 576, 591, 592, 609, 633, 660, 670, 676, 680, 690, 697, 713, 752
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125973.

Programs

  • Mathematica
    Do[If[PrimeQ[x^12 + x^11 - 1], Print[x]], {x, 1, 400}]
Select[Range[800],PrimeQ[#^12+#^11-1]&] (* Harvey P. Dale, Nov 08 2022 *)
  • PARI
    is(n)=isprime(n^12+n^11-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020

A125970 Numbers k for which k^13+k^12-1 is prime.

Original entry on oeis.org

38, 47, 51, 91, 102, 139, 150, 203, 207, 212, 218, 225, 237, 245, 263, 269, 278, 280, 283, 297, 300, 302, 303, 337, 357, 367, 370, 382, 404, 405, 408, 411, 425, 452, 456, 472, 496, 509, 514, 595, 605, 619, 626, 630, 670, 693, 707, 714, 735, 771, 773, 799, 854
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125973.

Programs

  • Mathematica
    Do[If[PrimeQ[x^13 + x^12 - 1], Print[x]], {x, 1, 600}]
  • PARI
    is(n)=isprime(n^13+n^12-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020

A125971 Numbers k for which k^14+k^13-1 is prime.

Original entry on oeis.org

6, 9, 11, 21, 29, 33, 36, 49, 64, 66, 68, 80, 110, 113, 144, 240, 266, 270, 309, 348, 365, 366, 394, 426, 438, 459, 471, 474, 479, 485, 501, 548, 553, 570, 593, 660, 684, 699, 704, 725, 729, 743, 783, 798, 801, 809, 815, 820, 824, 833, 841, 891, 900, 931, 968
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125973.

Programs

  • Mathematica
    Do[If[PrimeQ[x^14 + x^13 - 1], Print[x]], {x, 1, 600}]
  • PARI
    is(n)=isprime(n^14+n^13-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020
Previous Showing 11-20 of 27 results. Next

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

Content is available under The OEIS End-User License Agreement.