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 14 results. Next

A125885 Numbers k for which k^7+k^6-1 is prime.

Original entry on oeis.org

2, 4, 12, 17, 27, 39, 45, 46, 72, 94, 105, 106, 122, 126, 147, 149, 151, 156, 160, 161, 166, 169, 171, 172, 192, 194, 204, 205, 209, 230, 235, 242, 252, 260, 264, 266, 276, 280, 285, 306, 309, 319, 330, 335, 357, 371, 387, 400, 402, 411, 422, 439, 442, 451, 459
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881, A125882, A125883, A125884.

Programs

  • Mathematica
    Do[If[PrimeQ[x^7 + x^6 - 1], Print[x]], {x, 1, 200}]
  • PARI
    is(n)=isprime(n^7+n^6-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020

A125965 Numbers k for which k^8+k^7-1 is prime.

Original entry on oeis.org

2, 3, 4, 7, 8, 9, 18, 23, 32, 36, 41, 52, 54, 55, 56, 60, 68, 74, 80, 82, 87, 93, 107, 115, 140, 142, 146, 154, 162, 165, 170, 189, 227, 238, 253, 262, 263, 269, 276, 285, 300, 304, 305, 306, 308, 310, 315, 317, 332, 339, 350, 361, 363, 367, 371, 384, 386, 390
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125966-A125973.

Programs

A125973 Smallest k such that k^n + k^(n-1) - 1 is prime.

Original entry on oeis.org

2, 2, 2, 2, 2, 3, 2, 2, 14, 4, 7, 2, 38, 6, 7, 3, 4, 10, 2, 9, 74, 6, 10, 7, 4, 61, 20, 4, 5, 9, 6, 16, 6, 8, 2, 9, 4, 10, 2, 48, 44, 163, 9, 2, 95, 3, 27, 70, 6, 26, 57, 9, 6, 8, 207, 2, 27, 15, 45, 7, 69, 199, 55, 16, 2, 5, 12, 43, 137, 39, 9, 57, 5, 20, 4, 115, 2, 103, 45, 15, 20, 109
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Comments

The polynomial x^n + x^(n-1) - 1 is irreducible over the rationals (see Ljunggren link), so the Bunyakovsky conjecture implies that a(n) always exists. - Robert Israel, Nov 16 2016

Examples

			Consider n = 6. k^6 + k^5 - 1 evaluates to 1, 95, 971 for k = 1, 2, 3. Only the last of these numbers is prime, hence a(6) = 3.

Links

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125972, A126017.
Cf. A091997 (n such that a(n)=2).

Programs

  • Maple
    f:= proc(n) local k;
for k from 2 do if isprime(k^n+k^(n-1)-1) then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 16 2016
  • Mathematica
    a[n_] := For[k = 2, True, k++, If[PrimeQ[k^n + k^(n-1) - 1], Return[k]]];
Array[a, 100] (* Jean-François Alcover, Feb 26 2019 *)
  • PARI
    {m=82;for(n=1,m,k=1;while(!isprime(k^n+k^(n-1)-1),k++);print1(k,","))} \\ Klaus Brockhaus, Dec 17 2006

Extensions

Edited and extended by Klaus Brockhaus, Dec 17 2006

A125882 Numbers k for which k^4+k^3-1 is prime.

Original entry on oeis.org

2, 3, 6, 11, 13, 18, 24, 34, 38, 39, 43, 49, 52, 57, 58, 73, 74, 79, 90, 102, 104, 107, 113, 116, 122, 123, 126, 135, 139, 148, 155, 181, 183, 188, 193, 199, 203, 223, 234, 240, 247, 256, 261, 272, 273, 277, 286, 288, 298, 303, 329, 338, 344, 346, 357, 364, 366
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A045546, A125881, A125883, A125884, A125885.

Programs

  • Mathematica
    Do[If[PrimeQ[x^4 + x^3 - 1], Print[x]], {x, 1, 100}]
  • PARI
    is(n)=isprime(n^4+n^3-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020

A125883 Numbers k for which k^5+k^4-1 is prime.

Original entry on oeis.org

2, 4, 7, 9, 11, 13, 16, 17, 18, 26, 27, 29, 31, 33, 34, 38, 39, 40, 43, 47, 50, 57, 59, 65, 69, 70, 76, 81, 89, 90, 92, 93, 95, 103, 107, 109, 126, 128, 129, 138, 140, 148, 162, 167, 179, 182, 183, 192, 197, 206, 209, 211, 221, 223, 226, 228, 229, 230, 234, 240
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881, A125882, A125884, A125885.

Programs

  • Mathematica
    Do[If[PrimeQ[x^5 + x^4 - 1], Print[x]], {x, 1, 200}]
Select[Range[200],PrimeQ[#^5+#^4-1]&] (* Harvey P. Dale, Apr 10 2018 *)
  • PARI
    is(n)=isprime(n^5+n^4-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Amiram Eldar, Mar 18 2020

A125884 Numbers k for which k^6+k^5-1 is prime.

Original entry on oeis.org

3, 4, 5, 8, 9, 16, 18, 30, 34, 36, 41, 48, 49, 51, 54, 61, 65, 69, 76, 81, 86, 89, 90, 95, 101, 109, 120, 141, 170, 171, 178, 196, 221, 235, 238, 244, 260, 263, 273, 280, 291, 301, 303, 310, 311, 326, 350, 361, 375, 391, 398, 404, 405, 406, 423, 429, 431, 454, 456, 464, 479, 484, 485, 486, 489, 499
Offset: 1

Views

Author

Artur Jasinski, Dec 14 2006

Keywords

Links

Crossrefs

Cf. A000040, A045546, A125881, A125882, A125883, A125885.

Programs

  • Maple
    select(t -> isprime(t^6+t^5-1), [$1..1000]); # Robert Israel, Jan 08 2017
  • Mathematica
    Do[If[PrimeQ[x^6 + x^5 - 1], Print[x]], {x, 1, 200}]
  • PARI
    is(n)=isprime(n^6+n^5-1) \\ Charles R Greathouse IV, May 15 2013

Extensions

More terms from Robert Israel, Jan 08 2017

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

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
Showing 1-10 of 14 results. Next

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