A125259 -id:A125259 - cp's OEIS frontend

A067200 Numbers m such that m^3 + 2 is prime.

0, 1, 3, 5, 29, 45, 63, 65, 69, 71, 83, 105, 113, 123, 129, 143, 153, 171, 173, 189, 209, 215, 219, 231, 243, 245, 249, 263, 291, 299, 305, 311, 341, 363, 369, 395, 419, 425, 431, 435, 473, 483, 491, 495, 501, 503, 509, 515, 533, 549, 555, 561, 575, 579, 639

Offset: 1

Benoit Cloitre, Feb 19 2002

nonn

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A144953.

Other sequences of the type "Numbers m such that m^k + k - 1 is prime": A000040 (k=1), A005574 (k=2), this sequence (k=3), A125259 (k=4), A125260 (k=5), A125261 (k=6), A125262 (k=7), A125263 (k=8), A125264 (k=10), A125265 (k=11).

lst={}; Do[If[PrimeQ[n^3+2], AppendTo[lst, n]], {n, 0, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)
Select[Range[0,700],PrimeQ[#^3+2]&] (* Harvey P. Dale, Jul 27 2025 *)

is(n)=isprime(n^3 + 2) \\ Charles R Greathouse IV, Apr 29 2015

a(n) = (A144953(n) - 2)^(1/3). - Zak Seidov, Sep 16 2013

A125260 Numbers k such that k^5 + 4 is prime.

Original entry on oeis.org

1, 7, 9, 25, 39, 45, 73, 85, 99, 147, 163, 165, 169, 189, 213, 219, 223, 225, 249, 253, 259, 279, 333, 337, 385, 433, 457, 465, 469, 477, 499, 595, 639, 643, 655, 703, 709, 715, 729, 849, 853, 895, 969, 973, 979, 987, 1065, 1075, 1077, 1093, 1165, 1239, 1255

Offset: 1

Zak Seidov, Nov 26 2006

nonn

Carmine Suriano, Table of n, a(n) for n = 1..4431

Other sequences of the type "Numbers k such that k^j + j - 1 is prime": A000040 (j=1), A005574 (j=2), A067200 (j=3), A125259 (j=4), this sequence (j=5), A125261 (j=6), A125262 (j=7), A125263 (j=8), A125264 (j=10), A125265 (j=11)...

lst={};k=5;Do[If[PrimeQ[n^k+k-1], AppendTo[lst, n]], {n, 10^3}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
Select[Range[1300],PrimeQ[#^5+4]&] (* Harvey P. Dale, Oct 14 2019 *)

is(n)=isprime(n^5+4) \\ Charles R Greathouse IV, Feb 17 2017

A125262 Numbers k such that k^7 + 6 is prime.

Original entry on oeis.org

1, 13, 17, 23, 61, 73, 77, 101, 137, 215, 221, 283, 307, 317, 361, 431, 457, 473, 481, 641, 731, 767, 817, 881, 985, 1015, 1061, 1145, 1235, 1283, 1333, 1337, 1343, 1531, 1693, 1711, 1817, 1847, 1853, 1867, 1903, 1963, 2057, 2093, 2113, 2161, 2201, 2363

Offset: 1

Zak Seidov, Nov 26 2006

nonn

Carmine Suriano, Table of n, a(n) for n = 1..2374

Other sequences of the type "Numbers k such that k^j + j - 1 is prime": A000040 (j=1), A005574 (j=2), A067200 (j=3), A125259-A125265 (j=4..11).

lst={};k=7;Do[If[PrimeQ[n^k+k-1], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
Select[Range[2500],PrimeQ[#^7+6]&] (* Harvey P. Dale, May 05 2016 *)

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

A125265 Numbers k such that k^11 + 10 is prime.

Original entry on oeis.org

1, 7, 19, 21, 33, 69, 153, 157, 193, 253, 379, 391, 439, 543, 549, 559, 579, 609, 879, 937, 939, 993, 1063, 1083, 1107, 1119, 1191, 1209, 1267, 1281, 1287, 1333, 1537, 1617, 1797, 1819, 1923, 1971, 1987, 1989, 2041, 2061, 2073, 2101, 2103, 2343, 2373

Offset: 1

Zak Seidov, Nov 26 2006

nonn

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

Other sequences of the type "Numbers k such that k^j + j - 1 is prime": A000040 (j=1), A005574 (j=2), A067200 (j=3), A125259 (j=4), A125260 (j=5), A125261 (j=6), A125262 (j=7), A125263 (j=8), A125264 (j=10).

lst={};k=11;Do[If[PrimeQ[n^k+k-1], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
Select[Range[2500],PrimeQ[#^11+10]&] (* Harvey P. Dale, Jul 01 2015 *)

is(n)=isprime(n^11+10) \\ Charles R Greathouse IV, Feb 17 2017

A125261 Numbers k such that k^6 + 5 is prime.

Original entry on oeis.org

0, 18, 24, 114, 204, 216, 222, 246, 276, 312, 318, 372, 384, 426, 438, 468, 498, 582, 618, 654, 822, 888, 948, 984, 1182, 1188, 1272, 1278, 1284, 1374, 1446, 1536, 1674, 1782, 1788, 1794, 1806, 1812, 1896, 2034, 2058, 2088, 2124, 2154, 2232, 2238, 2376

Offset: 1

Zak Seidov, Nov 26 2006

nonn

Carmine Suriano, Table of n, a(n) for n = 1..2254

Other sequences of the type "Numbers k such that k^j + j - 1 is prime": A000040 (j=1), A005574 (j=2), A067200 (j=3), A125259 (j=4), A125260 (j=5), this sequence(j=6), A125262 (j=7), A125263 (j=8), A125264 (j=10), A125265 (j=11)..

lst={};k=6;Do[If[PrimeQ[n^k+k-1], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
Select[Range[0,2500],PrimeQ[#^6+5]&] (* Harvey P. Dale, Aug 29 2012 *)

is(n)=isprime(n^6+5) \\ Charles R Greathouse IV, Feb 17 2017

A125263 Numbers k such that k^8 + 7 is prime.

Original entry on oeis.org

0, 2, 4, 10, 66, 68, 86, 88, 134, 146, 200, 216, 250, 276, 306, 310, 410, 422, 472, 492, 506, 516, 538, 548, 550, 594, 638, 716, 746, 758, 862, 888, 942, 954, 964, 982, 992, 998, 1000, 1016, 1020, 1034, 1108, 1164, 1192, 1234, 1338, 1342, 1350, 1374, 1390

Offset: 1

Zak Seidov, Nov 26 2006

nonn

Carmine Suriano, Table of n, a(n) for n = 1..4683

Other sequences of the type "Numbers k such that k^j + j - 1 is prime": A000040 (j=1), A005574 (j=2), A067200 (j=3), A125259 (j=4), A125260 (j=5), A125261 (j=6), A125262 (j=7), this sequence (j=8), A125264 (j=10), A125265 (j=11)...

lst={};k=8;Do[If[PrimeQ[n^k+k-1], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
Select[Range[0,1500],PrimeQ[#^8+7]&] (* Harvey P. Dale, Sep 04 2024 *)

is(n)=isprime(n^8+7) \\ Charles R Greathouse IV, Feb 17 2017

A125264 Numbers k such that k^10 + 9 is prime.

Original entry on oeis.org

2, 8, 238, 310, 338, 442, 542, 688, 698, 872, 920, 1198, 1330, 1382, 1538, 1558, 1678, 1702, 1712, 1768, 1882, 2032, 2080, 2102, 2260, 2312, 2408, 2440, 2540, 2642, 3112, 3170, 3188, 3268, 3320, 3580, 3740, 3742, 3770, 3980, 4028, 4048, 4148, 4292, 4472

Offset: 1

Zak Seidov, Nov 26 2006

nonn

Carmine Suriano, Table of n, a(n) for n = 1..1524

Other sequences of the type "Numbers k such that k^j + j - 1 is prime": A000040 (j=1), A005574 (j=2), A067200 (j=3), A125259 (j=4), A125260 (j=5), A125261 (j=6), A125262 (j=7), A125263 (j=8), this sequence (j=10), A125265 (j=11).

lst={};k=10;Do[If[PrimeQ[n^k+k-1], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
Select[Range[5000],PrimeQ[#^10+9]&] (* Harvey P. Dale, Nov 17 2014 *)

is(n)=isprime(n^10+9) \\ Charles R Greathouse IV, Feb 17 2017

A127871 Numbers n such that n^4+1 and n^4+3 are twin primes.

Original entry on oeis.org

2, 16, 28, 34, 82, 118, 266, 296, 328, 436, 778, 1126, 1238, 1280, 1486, 1496, 1612, 1952, 2102, 2192, 2312, 2414, 2578, 2690, 2770, 2834, 2872, 3100, 3410, 3550, 3620, 3752, 4012, 4016, 4240, 4264, 4450, 4772, 5084, 5458, 5732, 5798, 5864, 6704, 7208

Offset: 1

Zak Seidov, Apr 05 2007

nonn

Intersection of A000068 and A125259.

Smallest k such that a(k+1) = a(k) + 2 is 364. - Altug Alkan, May 15 2018

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000068, A125259.

select(t -> isprime(t^4+1) and isprime(t^4+3), [seq(i,i=2..10^4,2)]); # Robert Israel, May 14 2018

Select[Range[0,200000,2],PrimeQ[ #^4+1]&&PrimeQ[ #^4+3]&]
Select[Range[7300],AllTrue[#^4+{1,3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 18 2019 *)

isok(n) = isprime(n^4+1) && isprime(n^4+3); \\ Michel Marcus, May 15 2018

A147515 Numbers n with property that (2n)^4+3 is prime.

Original entry on oeis.org

0, 1, 4, 8, 11, 13, 14, 17, 22, 31, 34, 38, 41, 46, 52, 55, 59, 64, 67, 83, 92, 101, 106, 133, 143, 148, 157, 164, 175, 178, 188, 203, 214, 218, 230, 235, 253, 260, 266, 281, 290, 319, 325, 326, 340, 346, 361, 367, 370, 389, 406, 410, 412, 431, 448, 454, 461, 466

Offset: 1

Zak Seidov, Nov 05 2008

nonn

Zak Seidov, Table of n, a(n) for n=1..1000

Cf. A125259.

Select[Range[0,500],PrimeQ[(2#)^4+3]&] (* Harvey P. Dale, Jul 18 2019 *)

isok(n) = isprime((2*n)^4+3); \\ Michel Marcus, Oct 15 2013

a(n) = A125259(n)/2.

cp's OEIS Frontend

A067200 Numbers m such that m^3 + 2 is prime.

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A125260 Numbers k such that k^5 + 4 is prime.

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A125262 Numbers k such that k^7 + 6 is prime.

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A125265 Numbers k such that k^11 + 10 is prime.

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Mathematica

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A125261 Numbers k such that k^6 + 5 is prime.

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A125263 Numbers k such that k^8 + 7 is prime.

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Mathematica

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A125264 Numbers k such that k^10 + 9 is prime.

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Mathematica

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A127871 Numbers n such that n^4+1 and n^4+3 are twin primes.

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Maple

Mathematica

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A147515 Numbers n with property that (2n)^4+3 is prime.

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