A124178 -id:A124178 - cp's OEIS frontend

A244376 Numbers k such that 1 + k + k^3 + k^5 + k^7 + k^9 + k^11 is prime.

1, 2, 10, 40, 47, 55, 62, 121, 137, 152, 167, 201, 233, 278, 290, 293, 313, 333, 370, 382, 430, 452, 460, 506, 546, 555, 613, 625, 642, 675, 705, 711, 752, 767, 793, 797, 831, 835, 837, 872, 878, 891, 906, 917, 923, 978, 985, 1005, 1012, 1017, 1018, 1021

Offset: 1

Vincenzo Librandi, Jun 27 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1400

Cf. A127936.

Cf. numbers n such that 1+n+n^3 + ... + n^k, with k odd: A006093 (k=1), A049407 (k=3), A124154 (k=5), A124150 (k=7), A124163 (k=9), this sequence (k=11), A124164 (k=13), A244377 (k=15), A244378 (k=17), A124178 (k=19), A244379 (k=21), A124181 (k=23), A244380 (k=25), A124185 (k=27), A244383 (k=29), A124186 (k=31), A244384 (k=33), A124187 (k=35), A244385 (k=37), A124189 (k=39), A244386 (k=41), A124200 (k=43), A244387 (k=45), A124205 (k=47), A244388 (k=49), A124206 (k=51), A244389 (k=53), A124207 (k=55), A244390 (k=57), A124208 (k=59), A244391 (k=61), A124209 (k=63).

[n: n in [0..1500] | IsPrime(s) where s is 1+&+[n^i: i in [1..11 by 2]]];

Select[Range[4000], PrimeQ[Total[#^Range[1, 11, 2]] + 1] &]

isok(n) = isprime(1 + n + n^3 + n^5 + n^7 + n^9 + n^11); \\ Michel Marcus, Jun 27 2014

i,n = var('i,n')
[n for n in (1..2000) if is_prime(1+(n^(2*i+1)).sum(i,0,5))] # Bruno Berselli, Jun 27 2014

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

Original entry on oeis.org

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

A126916 Numbers n such that 1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^20 + n^22 + n^23 is prime.

Original entry on oeis.org

1, 2, 11, 23, 47, 64, 77, 80, 103, 251, 290, 321, 331, 335, 375, 382, 387, 403, 507, 568, 590, 594, 649, 801, 805, 828, 830, 840, 847, 854, 905, 925, 926, 959, 982, 986, 1034, 1086, 1094, 1102, 1122, 1129, 1147, 1160, 1391

Offset: 1

Artur Jasinski, Dec 31 2006

nonn

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^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^20 + n^22 + n^23], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[1400],PrimeQ[Total[#^Range[2,22,2]]+1+#^23]&] (* Harvey P. Dale, Oct 04 2018 *)

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^22+n^23) \\ Charles R Greathouse IV, Feb 17 2017

A124401 Indices where 2 occurs in A124151.

Original entry on oeis.org

3, 5, 8, 9, 11, 15, 21, 39, 50, 63, 83, 95, 99, 173, 350, 854, 1308, 1769, 2903, 5250, 5345, 5639, 6195, 7239, 21368, 41669, 47684, 58619, 63515, 69468, 70539, 133508, 134993, 187160, 493095

Offset: 1

Artur Jasinski, Dec 14 2006

Does 2 occur infinitely often in A124151?

The sum in A124151 is 1+n if k=1, and 1+k*(k^(2n)-1)/(k^2-1) if k>1. The indices of A124151(n)=2 are where k=1 is avoided, but where k=2 leads to a prime, i.e., where 1+n is not prime but 1+2*(4^n-1)/3 = (2^(2n+1)+1)/3 is prime. Therefore this sequence here is constructed by taking all n=(A000978(i)-1)/2 (the members of A127936), and eliminating cases with 1+n in A000040. - R. J. Mathar, Feb 03 2010

Cf. A006093, A124151, A124154, A124163, A124164, A124178, A124181, A124185-A124187, A124189, A124200, A124205-A124209.

f[n_] := Block[{k = 1}, While[ !PrimeQ[ Sum[k^(2j - 1), {j, n}] + 1] && k < 3, k++ ]; k]; lst = {}; Do[ If[f@n == 2, Print[n]; AppendTo[lst, n]], {n, 9250}]; lst (* Robert G. Wilson v, Dec 17 2006 *)

is(n) = !isprime(n+1) && isprime(1 + 2*(4^n-1)/3); \\ Amiram Eldar, Oct 24 2024

A127936 \ A006093. - R. J. Mathar, Feb 03 2010

More terms from Robert G. Wilson v, Dec 17 2006

a(24)-a(35) from R. J. Mathar, Feb 03 2010

A124151 Smallest k such that 1 + Sum{j=1..n} k^(2*j-1) is prime.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 10, 2, 2, 1, 2, 1, 48, 182, 2, 1, 60, 1, 10, 42, 2, 1, 102, 12, 4, 12, 110, 1, 12, 1, 100, 5, 28, 18, 144, 1, 102, 9, 2, 1, 30, 1, 186, 110, 130, 1, 566, 23, 1234, 2, 12, 1, 336, 103, 142, 341, 1104, 1, 444, 1, 22, 119, 2, 45, 14, 1, 84, 23, 238, 1, 936, 1, 78, 12

Offset: 1

Artur Jasinski, Dec 13 2006, Dec 14 2006

nonn

a(n) = 1 if and only if n is in A006093 (primes minus 1), so 1 occurs infinitely often.

			Consider n = 7. 1 + Sum{j=1...7} k^(2*j-1) evaluates to 8, 10923, 1793614, 71582789, 1271565756, 13433856703, 98907531458, 558482096649, 2573639151184, 10101010101011 for k = 1, ..., 10. Only the last of these numbers, 1+10+10^3+10^5+10^7+10^9+10^11+10^13 = 10101010101011, is prime, hence a(7) = 10.

Cf. A006093, A124205-A124209, A124164, A124178, A124181, A124185-A124187, A124189, A124200, A124154, A124163.

f[n_] := Block[{k = 1}, While[ !PrimeQ[Sum[k^(2j - 1), {j, n}] + 1], k++ ]; k]; Array[f, 74] (* Robert G. Wilson v, Dec 17 2006 *)

a(n)={my(k=1);while(!isprime(1+sum(j=1,n,k^(2*j-1))),k++); k} \\ Klaus Brockhaus, Dec 16 2006

Edited and extended by Klaus Brockhaus, Dec 16 2006

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

cp's OEIS Frontend

A244376 Numbers k such that 1 + k + k^3 + k^5 + k^7 + k^9 + k^11 is prime.

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

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A126916 Numbers n such that 1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^20 + n^22 + n^23 is prime.

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A124401 Indices where 2 occurs in A124151.

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A124151 Smallest k such that 1 + Sum{j=1..n} k^(2*j-1) 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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A126906 Smallest k such that 1 + k^(2n+1) + Sum_{j=1..n} k^(2j) is prime.