A124178 -id:A124178 - cp's OEIS frontend

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

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

A126018 Smallest prime of the form 1 + Sum{j=1..n} k^(2*j-1).

Original entry on oeis.org

2, 3, 43, 5, 683, 7, 10101010101011, 43691, 174763, 11, 2796203, 13, 1074532291189456211731158116986854092943409, 10518179715343122711873674826619717982095485405484801996888751, 715827883, 17, 47765234780450752737667634787440955821061405946096137816061

Offset: 1

Artur Jasinski, Dec 14 2006

nonn

Primes arising in A124151.

If n=(prime number-1) then a(n) = prime(n). - Artur Jasinski, Dec 23 2006

			Consider n = 8. 1 + Sum{j=1...8} k^(2*j-1) evaluates to 9 for k = 1 and to 43691 for k = 2. 9 is composite but 43691 is prime, hence a(8) = 1+2+2^3+2^5+2^7+2^9+2^11+2^13+2^15 = 43691.

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

Table[k=0; Until[PrimeQ[p=1+Sum[k^(2j-1),{j,n}]], k++]; p, {n, 17}] (* James C. McMahon, Dec 23 2024 *)

{for(n=1,14,k=1;while(!isprime(s=1+sum(j=1,n,k^(2*j-1))),k++);print1(s,","))} \\ Klaus Brockhaus, Dec 16 2006

Edited and extended by Klaus Brockhaus, Dec 16 2006

a(15)-a(17) from James C. McMahon, Dec 23 2024

cp's OEIS Frontend

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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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.

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A126018 Smallest prime of the form 1 + Sum{j=1..n} k^(2*j-1).

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