A125261 -id:A125261 - 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

A125259 Numbers k such that k^4 + 3 is prime.

Original entry on oeis.org

0, 2, 8, 16, 22, 26, 28, 34, 44, 62, 68, 76, 82, 92, 104, 110, 118, 128, 134, 166, 184, 202, 212, 266, 286, 296, 314, 328, 350, 356, 376, 406, 428, 436, 460, 470, 506, 520, 532, 562, 580, 638, 650, 652, 680, 692, 722, 734, 740, 778, 812, 820, 824, 862, 896, 908

Offset: 1

Zak Seidov, Nov 26 2006

nonn

Carmine Suriano, Table of n, a(n) for n = 1..5860

Other sequences of the type "Numbers k such that k^j + j - 1 is prime": A000040 (j=1), A005574 (j=2), A067200 (j=3), this sequence (j=4), A125260 (j=5), A125261 (j=6), A125262 (j=7), A125263 (j=8), A125264 (j=10), A125265 (j=11)...

Select[Range[0,1000],PrimeQ[#^4+3]&] (* Harvey P. Dale, Aug 02 2023 *)

isok(n, k=4) = isprime(n^k + k - 1); \\ Michel Marcus, Oct 11 2013

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

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

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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A125259 Numbers k such that k^4 + 3 is prime.

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

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

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

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