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 31-38 of 38 results.

A126909 Numbers n such that 1 + n^2 + n^4 + n^6 + n^8 + n^9 is prime.

Original entry on oeis.org

2, 18, 48, 56, 116, 120, 128, 146, 194, 198, 200, 230, 266, 278, 282, 288, 324, 362, 372, 390, 396, 420, 434, 458, 488, 576, 594, 708, 714, 728, 740, 774, 818, 830, 860, 888, 896, 912, 914, 990, 996, 1002, 1008, 1010, 1016, 1044, 1124, 1128, 1140, 1146, 1260
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Links

Crossrefs

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^9], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[1300],PrimeQ[1+#^2+#^4+#^6+#^8+#^9]&] (* Harvey P. Dale, Apr 25 2020 *)
  • PARI
    is(n)=isprime(1+n^2+n^4+n^6+n^8+n^9) \\ Charles R Greathouse IV, Jun 13 2017

A126910 Numbers k such that 1 + k^2 + k^4 + k^6 + k^8 + k^10 + k^11 is prime.

Original entry on oeis.org

1, 2, 3, 35, 48, 77, 97, 105, 111, 112, 122, 128, 161, 168, 175, 216, 231, 255, 271, 276, 297, 338, 361, 370, 378, 422, 485, 513, 525, 558, 622, 658, 661, 662, 667, 675, 700, 718, 725, 742, 753, 766, 770, 795, 796, 833, 875, 886, 921, 993, 1027, 1066, 1078
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Links

Crossrefs

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^11], AppendTo[a, n]], {n, 1, 1400}]; a
  • PARI
    is(n)=isprime(1+n^2+n^4+n^6+n^8+n^10+n^11) \\ Charles R Greathouse IV, Jun 13 2017

A126911 Numbers k such that 1 + k^2 + k^4 + k^6 + k^8 + k^10 + k^12 + k^13 is prime.

Original entry on oeis.org

10, 24, 60, 148, 174, 180, 268, 274, 280, 294, 346, 472, 484, 516, 522, 598, 654, 804, 834, 856, 858, 898, 994, 1012, 1036, 1054, 1066, 1102, 1168, 1272, 1294, 1338, 1342, 1368, 1420, 1462, 1500, 1536, 1564, 1588, 1608, 1624, 1710, 1746, 1786, 1792, 1822, 1992
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Links

Crossrefs

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^13], AppendTo[a, n]], {n, 1, 1400}]; a
  • PARI
    is(n)=isprime(1+n^2+n^4+n^6+n^8+n^10+n^12+n^13) \\ Charles R Greathouse IV, Jun 13 2017
  • Python
    from sympy import isprime
def ok(k): return isprime(1+sum(k**i for i in [2, 4, 6, 8, 10, 12, 13]))
print([k for k in range(2000) if ok(k)]) # Michael S. Branicky, Oct 24 2021

A126912 Numbers k such that 1 + k^2 + k^4 + k^6 + k^8 + k^10 + k^12 + k^14 + k^15 is prime.

Original entry on oeis.org

17, 47, 71, 72, 95, 99, 107, 113, 123, 134, 135, 147, 159, 239, 257, 261, 263, 278, 299, 324, 348, 435, 477, 500, 521, 534, 536, 546, 563, 567, 585, 633, 635, 642, 716, 737, 750, 753, 852, 905, 974, 1088, 1178, 1181, 1205, 1272, 1283, 1298, 1311, 1331, 1356
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Links

Crossrefs

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^15], AppendTo[a, n]], {n, 1, 1400}]; a
  • PARI
    is(n)=isprime(1+n^2+n^4+n^6+n^8+n^10+n^12+n^14+n^15) \\ Charles R Greathouse IV, Jun 13 2017

A126913 Numbers n such that 1 + k^2 + k^4 + k^6 + k^8 + k^10 + k^12 + k^14 + k^16 + k^17 is prime.

Original entry on oeis.org

2, 22, 38, 102, 128, 130, 172, 232, 250, 292, 378, 404, 424, 458, 472, 490, 510, 600, 608, 702, 774, 802, 868, 888, 938, 950, 1010, 1140, 1204, 1220, 1274, 1294, 1328, 1372, 1394, 1398, 1402, 1412, 1418, 1502, 1564, 1580, 1602, 1670, 1692, 1792, 1800
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Links

Crossrefs

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^17], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[2000],PrimeQ[Total[#^{0,2,4,6,8,10,12,14,16,17}]]&] (* Harvey P. Dale, Jan 07 2023 *)
  • PARI
    is(n)=isprime(1+n^2+n^4+n^6+n^8+n^10+n^12+n^14+n^16+n^17) \\ Charles R Greathouse IV, Jun 13 2017

A126914 Numbers n such that 1 + k^2 + k^4 + k^6 + k^8 + k^10 + k^12 + k^14 + k^16 + k^18 + k^19 is prime.

Original entry on oeis.org

1, 9, 37, 40, 60, 69, 85, 114, 147, 156, 174, 183, 255, 289, 312, 324, 336, 349, 361, 373, 418, 451, 493, 499, 511, 520, 534, 549, 649, 657, 673, 676, 715, 741, 787, 855, 862, 874, 883, 888, 897, 952, 960, 1021, 1087, 1092, 1104, 1126, 1141, 1147, 1171, 1209
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Links

Crossrefs

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^19], AppendTo[a, n]], {n, 1, 1400}]; a
  • PARI
    is(n)=isprime(1+n^2+n^4+n^6+n^8+n^10+n^12+n^14+n^16+n^18+n^19) \\ Charles R Greathouse IV, Jun 13 2017

A126915 Numbers k such that 1 + k^2 + k^4 + k^6 + k^8 + k^10 + k^12 + k^14 + k^16 + k^18 + k^20 + k^21 is prime.

Original entry on oeis.org

2, 6, 12, 60, 68, 138, 270, 446, 488, 620, 656, 798, 872, 942, 950, 1136, 1140, 1256, 1400, 1418, 1506, 1638, 1776, 1922, 1992, 2070, 2082, 2096, 2220, 2346, 2462, 2580, 2606, 2916
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Links

Crossrefs

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

Programs

  • Magma
    [k:k in [1..3000]| IsPrime(1+k^2+k^4+k^6+k^8+k^10+k^12+k^14+k^16+ k^18+k^20 +k^21)]; // Marius A. Burtea, Feb 11 2020
  • Mathematica
    a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^20 + n^21], AppendTo[a, n]], {n, 1, 1400}]; a
  • PARI
    is(n)=isprime(1+n^2+n^4+n^6+n^8+n^10+n^12+n^14+n^16+n^18+n^20+n^21) \\ Charles R Greathouse IV, Jun 13 2017

A245476 Least number k > 1 such that k^n + k + 1 is prime, or 0 if no such number exists.

Original entry on oeis.org

2, 2, 2, 2, 0, 2, 2, 0, 3, 3, 0, 2, 5, 0, 2, 2, 0, 2, 8, 0, 6, 3, 0, 6, 15, 0, 6, 2, 0, 2, 23, 0, 23, 56, 0, 15, 114, 0, 14, 11, 0, 3, 14, 0, 29, 110, 0, 21, 9, 0, 53, 59, 0, 6, 2, 0, 3, 29, 0, 71, 21, 0, 146, 17, 0, 35, 2, 0, 9, 6, 0, 77, 41, 0, 27, 176, 0, 153, 21, 0, 39, 32, 0, 2, 314, 0, 3, 5, 0, 66, 44, 0, 234
Offset: 1

Views

Author

Derek Orr, Jul 23 2014

Keywords

Comments

Except for a(2), a(n) = 0 if n == 2 mod 3 (A016789).
It appears that this is an "if and only if".
a(n) = 2 if and only if n is in A057732.
Many terms in the linked table correspond to probable primes. If n == 2 mod 3 then k^2+k+1 divides k^n+k+1. This is why a(n) = 0 if n > 2 and n == 2 mod 3. - Jens Kruse Andersen, Jul 28 2014

Examples

			2^9 + 2 + 1 = 515 is not prime. 3^9 + 3 + 1 = 19687 is prime. Thus a(9) = 3.

Links

Crossrefs

Cf. A127599, A016789, A057732.
Cf. Numbers n such that n^s + n + 1 is prime: A005097 (s = 1), A002384 (s = 2), A049407 (s = 3), A049408 (s = 4), A075723 (s = 6), A075722 (s = 7), A075720 (s = 9), A075719 (s = 10), A075718 (s = 12), A075717 (s = 13), A075716 (s = 15), A075715 (s = 16), A075714 (s = 18), A075713 (s = 19).

Programs

  • Maple
    f:= proc(n) local k;
   if n mod 3 = 2 and n > 2 then return 0 fi;
   for k from 2 to 10^6 do
      if isprime(k^n+k+1) then return k fi
   od:
  error("no solution found for n = %1",n);
end proc:
seq(f(n),n=1..100); # Robert Israel, Jul 27 2014
  • PARI
    a(n) = if(n>2&&n==Mod(2, 3), return(0)); k=2; while(!ispseudoprime(k^n+k+1), k++); k
vector(150, n, a(n)) \\ Derek Orr with corrections and improvements from Colin Barker, Jul 23 2014
Previous Showing 31-38 of 38 results.

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