A126916 -id:A126916 - cp's OEIS frontend

A126908 Numbers k such that 1 + k^2 + k^4 + k^6 + k^7 is prime.

1, 4, 13, 15, 24, 30, 37, 40, 55, 93, 138, 139, 148, 153, 154, 159, 160, 165, 184, 195, 204, 223, 258, 303, 355, 360, 373, 459, 472, 475, 510, 519, 534, 577, 594, 607, 615, 627, 658, 672, 688, 723, 735, 739, 795, 805, 807, 817, 819, 820, 847, 874, 879, 904

Offset: 1

Artur Jasinski, Dec 31 2006

nonn

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^7], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[1000],PrimeQ[1+#^2+#^4+#^6+#^7]&] (* Harvey P. Dale, Jan 15 2016 *)

is(n)=isprime(1+n^2+n^4+n^6+n^7) \\ Charles R Greathouse IV, Feb 17 2017

A126906 Smallest k such that 1 + k^(2n+1) + Sum_{j=1..n} k^(2j) is prime.

Original entry on oeis.org

1, 2, 1, 2, 1, 10, 17, 2, 1, 2, 1, 94, 122, 22, 1, 80, 1, 4, 6, 2, 1, 242, 3, 6, 5, 80, 1, 12, 1, 82, 96, 2, 7, 188, 1, 136, 69, 158, 1, 2, 1, 954, 50, 118, 1, 570, 14, 90, 45, 6, 1, 228, 38, 4, 6, 22, 1, 12, 1, 580, 86, 336, 24, 768, 1, 1170, 408, 340, 1, 896

Offset: 1

Artur Jasinski, Dec 31 2006

nonn

1 is a term if and only if number of terms in polynomial is prime.

Amiram Eldar, Table of n, a(n) for n = 1..250

Cf. A124151, A119863, A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

a[n_]: = Module[{k = 1}, While[!PrimeQ[1 + k^(2*n+1) + Sum[k^(2*j), {j, 1, n}]], k++]; k]; Array[a, 30] (* Amiram Eldar, Mar 13 2020 *)

a(n) = my(k = 1); while(! isprime(1 + k^(2*n+1) + sum(j=1, n, k^(2*j))), k++); k; \\ Michel Marcus, Mar 13 2020

More terms from Amiram Eldar, Mar 13 2020

A126907 Numbers n such that 1 + n^2 + n^4 + n^5 is prime.

Original entry on oeis.org

2, 4, 6, 8, 12, 18, 32, 34, 68, 70, 78, 88, 110, 114, 116, 118, 120, 122, 132, 134, 142, 150, 172, 180, 186, 190, 210, 216, 238, 246, 254, 272, 294, 322, 362, 376, 380, 386, 388, 408, 476, 500, 502, 506, 508, 520, 530, 542, 564, 584, 588, 590, 616, 620, 632

Offset: 1

Artur Jasinski, Dec 31 2006

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^5], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[700],PrimeQ[1+#^2+#^4+#^5]&] (* Harvey P. Dale, Jun 24 2018 *)

is(n)=isprime(1+n^2+n^4+n^5) \\ Charles R Greathouse IV, Jun 13 2017

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

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

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 *)

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

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^11], AppendTo[a, n]], {n, 1, 1400}]; a

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

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

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

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

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

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

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

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

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

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 *)

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

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

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

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

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

[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

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

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

cp's OEIS Frontend

A126908 Numbers k such that 1 + k^2 + k^4 + k^6 + k^7 is prime.

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A126906 Smallest k such that 1 + k^(2*n+1) + Sum_{j=1..n} k^(2*j) is prime.

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A126907 Numbers n such that 1 + n^2 + n^4 + n^5 is prime.

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

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

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

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

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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.

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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.

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A126906 Smallest k such that 1 + k^(2n+1) + Sum_{j=1..n} k^(2j) is prime.