A162862 -id:A162862 - cp's OEIS frontend

A217083 Numbers n such that (n^67-1)/(n-1) is prime.

46, 122, 238, 304, 314, 315, 328, 332, 346, 372, 382, 426, 440, 491, 496, 510, 524, 528, 566, 638, 733, 826, 1016, 1054, 1071, 1214, 1309, 1338, 1388, 1401, 1457, 1512, 1536, 1582, 1624, 1718, 1773, 1814, 1816, 1825, 1952, 1985, 2021, 2072, 2308, 2349, 2449, 2481

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

Select[Range[2, 2500], PrimeQ[(#^67 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^67-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217084 Numbers n such that (n^71-1)/(n-1) is prime.

Original entry on oeis.org

3, 6, 17, 24, 37, 89, 132, 374, 387, 402, 421, 435, 453, 464, 490, 516, 708, 736, 919, 947, 981, 1033, 1067, 1170, 1195, 1253, 1284, 1349, 1385, 1409, 1479, 1709, 1724, 1726, 1735, 1875, 1950, 1984, 2012, 2070, 2124, 2133, 2161, 2194, 2424, 2432, 2459, 2531, 2552

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

Select[Range[2, 1000], PrimeQ[(#^71 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^71-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217085 Numbers n such that (n^73-1)/(n-1) is prime.

Original entry on oeis.org

11, 15, 75, 114, 195, 215, 295, 335, 378, 559, 566, 650, 660, 832, 871, 904, 966, 1021, 1112, 1203, 1334, 1433, 1485, 1724, 1822, 1959, 1998, 2115, 2154, 2432, 2465, 2486, 2544, 2559, 2564, 2575, 2611, 2681, 2705, 2735, 2754, 2806, 2880, 3158, 3222, 3306, 3368

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

nonn

G. C. Greubel, Table of n, a(n) for n = 1..5000 (terms 1..500 from Vincenzo Librandi)

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

Select[Range[2, 1000], PrimeQ[(#^73 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^73-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217086 Numbers n such that (n^79-1)/(n-1) is prime.

Original entry on oeis.org

22, 112, 140, 158, 170, 254, 271, 330, 334, 354, 390, 483, 528, 560, 565, 714, 850, 888, 924, 929, 933, 935, 970, 1019, 1047, 1141, 1266, 1338, 1359, 1376, 1412, 1485, 1504, 1542, 1598, 1607, 1618, 1747, 1773, 1814, 1843, 2087, 2088, 2100, 2167, 2186, 2233, 2311

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..500

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

Select[Range[2, 1000], PrimeQ[(#^79 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^79-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217087 Numbers n such that (n^83-1)/(n-1) is prime.

Original entry on oeis.org

41, 146, 386, 593, 667, 688, 906, 927, 930, 1025, 1032, 1111, 1410, 1437, 1638, 1829, 1960, 2045, 2381, 2384, 2618, 2807, 2909, 3059, 3164, 3268, 3370, 3783, 3861, 4043, 4054, 4198, 4284, 4539, 4934, 4968, 4992, 5009, 5047, 5049, 5111, 5217, 5237, 5342, 5367

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

Select[Range[2, 1000], PrimeQ[(#^83 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^83-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A250177 Numbers n such that Phi_21(n) is prime, where Phi is the cyclotomic polynomial.

Original entry on oeis.org

3, 6, 7, 12, 22, 27, 28, 35, 41, 59, 63, 69, 112, 127, 132, 133, 136, 140, 164, 166, 202, 215, 218, 276, 288, 307, 323, 334, 343, 377, 383, 433, 474, 479, 516, 519, 521, 532, 538, 549, 575, 586, 622, 647, 675, 680, 692, 733, 790, 815, 822, 902, 909, 911, 915, 952, 966, 1025, 1034, 1048, 1093

Offset: 1

Eric Chen, Dec 24 2014

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A008864 (1), A006093 (2), A002384 (3), A005574 (4), A049409 (5), A055494 (6), A100330 (7), A000068 (8), A153439 (9), A250392 (10), A162862 (11), A246397 (12), A217070 (13), A250174 (14), A250175 (15), A006314 (16), A217071 (17), A164989 (18), A217072 (19), A250176 (20), this sequence (21), A250178 (22), A217073 (23), A250179 (24), A250180 (25), A250181 (26), A153440 (27), A250182 (28), A217074 (29), A250183 (30), A217075 (31), A006313 (32), A250184 (33), A250185 (34), A250186 (35), A097475 (36), A217076 (37), A250187 (38), A250188 (39), A250189 (40), A217077 (41), A250190 (42), A217078 (43), A250191 (44), A250192 (45), A250193 (46), A217079 (47), A250194 (48), A250195 (49), A250196 (50), A217080 (53), A217081 (59), A217082 (61), A006315 (64), A217083 (67), A217084 (71), A217085 (73), A217086 (79), A153441 (81), A217087 (83), A217088 (89), A217089 (97), A006316 (128), A153442 (243), A056994 (256), A056995 (512), A057465 (1024), A057002 (2048), A088361 (4096), A088362 (8192), A226528 (16384), A226529 (32768), A226530 (65536), A251597 (131072), A244150 (524287), A243959 (1048576).

Cf. A085398 (Least k>1 such that Phi_n(k) is prime).

a250177[n_] := Select[Range[n], PrimeQ@Cyclotomic[21, #] &]; a250177[1100] (* Michael De Vlieger, Dec 25 2014 *)

{is(n)=isprime(polcyclo(21,n))};
for(n=1,100, if(is(n)==1, print1(n, ", "), 0)) \\ G. C. Greubel, Apr 14 2018

A240693 Primes p such that p^10 + p^9 + p^8 + p^7 + p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 is prime.

Original entry on oeis.org

5, 17, 53, 137, 229, 389, 467, 619, 709, 787, 1091, 1103, 1213, 1249, 1433, 1459, 1601, 1993, 2029, 2039, 2087, 2089, 2393, 2687, 3217, 3299, 3529, 3547, 3691, 3793, 4019, 4091, 4099, 4231, 4507, 4561, 4679, 5351, 5399, 5471, 5521, 5581, 5669, 5783, 5813, 5861, 5939, 6247, 6841, 6899, 6961

Offset: 1

Derek Orr, Apr 10 2014

nonn

These are the primes in A162862.

			5^10 + 5^9 + 5^8 + 5^7 + 5^6 + 5^5 + 5^4 + 5^3 + 5^2 + 5 + 1 = 12207031 is prime. Thus, 5 is a term of this sequence.

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Cf. A162862.

Select[Prime[Range[200]], PrimeQ[1 + Sum[#^i, {i, 10}]] &] (* Alonso del Arte, Apr 11 2014 *)
Select[Prime[Range[900]],PrimeQ[Total[#^Range[0,10]]]&] (* Harvey P. Dale, Oct 11 2023 *)

for(n=1,10^4,if(ispseudoprime(n^10+n^9+n^8+n^7+n^6+n^5+n^4+n^3+n^2+n+1)&&ispseudoprime(n),print(n)))

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n) and isprime(n**10+n**9+n**8+n**7+n**6+n**5+n**4+n**3+n**2+n+1)}

A286301 Primes of the form p^10 + p^9 + p^8 + p^7 + p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime.

Original entry on oeis.org

12207031, 2141993519227, 178250690949465223, 2346320474383711003267, 398341412240537151131351, 79545183674814239059370551, 494424256962371823779424877, 8271964541879648991904246901, 32142180034067960734115528951, 91264002187709396686868598317

Offset: 1

Hartmut F. W. Hoft, May 05 2017

nonn

			Prime number 12207031 = Sum_{i=0..10} 5^i is the first in the sequence since 23 divides 88573 = Sum_{i=0..10} 3^i as well as 2047 = Sum_{i=0..10} 2^i.

Subsequence of A060885, A162861 and A193574.

Cf. A162862, A198244, A240693.

a286301[n_] := Select[Map[(Prime[#]^11-1)/(Prime[#]-1)&, Range[n]], PrimeQ]
a286301[150] (* data *)

A250175 Numbers n such that Phi_15(n) is prime, where Phi is the cyclotomic polynomial.

Original entry on oeis.org

2, 3, 11, 17, 23, 43, 46, 52, 53, 61, 62, 78, 84, 88, 89, 92, 99, 108, 123, 124, 141, 146, 154, 156, 158, 163, 170, 171, 182, 187, 202, 217, 219, 221, 229, 233, 238, 248, 249, 253, 264, 274, 275, 278, 283, 285, 287, 291, 296, 302, 309, 314, 315, 322, 325, 342, 346, 353, 356, 366, 368, 372, 377, 380, 384, 394, 404, 406, 411, 420, 425

Offset: 1

Eric Chen, Dec 24 2014

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A008864 (1), A006093 (2), A002384 (3), A005574 (4), A049409 (5), A055494(6), A100330 (7), A000068 (8), A153439 (9), A246392 (10), A162862(11), A246397 (12), A217070 (13), A006314 (16), A217071 (17), A164989(18), A217072 (19), A217073 (23), A153440 (27), A217074 (29), A217075(31), A006313 (32), A097475 (36), A217076 (37), A217077 (41), A217078(43), A217079 (47), A217080 (53), A217081 (59), A217082 (61), A006315(64), A217083 (67), A217084 (71), A217085 (73), A217086 (79), A153441(81), A217087 (83), A217088 (89), A217089 (97), A006316 (128), A153442(243), A056994 (256), A056995 (512), A057465 (1024), A057002 (2048), A088361 (4096), A088362 (8192), A226528 (16384), A226529 (32768), A226530(65536).

Select[Range[600], PrimeQ[Cyclotomic[15, #]] &] (* Vincenzo Librandi, Jan 16 2015 *)

isok(n) = isprime(polcyclo(15, n)); \\ Michel Marcus, Jan 16 2015

More terms from Vincenzo Librandi, Jan 16 2015

A250176 Numbers n such that Phi_20(n) is prime, where Phi is the cyclotomic polynomial.

Original entry on oeis.org

4, 9, 11, 16, 19, 26, 34, 45, 54, 70, 86, 91, 96, 101, 105, 109, 110, 119, 120, 126, 129, 139, 141, 149, 171, 181, 190, 195, 215, 229, 260, 276, 299, 305, 309, 311, 314, 319, 334, 339, 369, 375, 414, 420, 425, 444, 470, 479, 485, 506, 519, 534, 540, 550

Offset: 1

Eric Chen, Dec 24 2014

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A008864 (1), A006093 (2), A002384 (3), A005574 (4), A049409 (5), A055494(6), A100330 (7), A000068 (8), A153439 (9), A246392 (10), A162862(11), A246397 (12), A217070 (13), A006314 (16), A217071 (17), A164989(18), A217072 (19), A217073 (23), A153440 (27), A217074 (29), A217075(31), A006313 (32), A097475 (36), A217076 (37), A217077 (41), A217078(43), A217079 (47), A217080 (53), A217081 (59), A217082 (61), A006315(64), A217083 (67), A217084 (71), A217085 (73), A217086 (79), A153441(81), A217087 (83), A217088 (89), A217089 (97), A006316 (128), A153442(243), A056994 (256), A056995 (512), A057465 (1024), A057002 (2048), A088361 (4096), A088362 (8192), A226528 (16384), A226529 (32768), A226530(65536).

Select[Range[600], PrimeQ[Cyclotomic[20, #]] &] (* Vincenzo Librandi, Jan 16 2015 *)

isok(n) = isprime(polcyclo(20, n)); \\ Michel Marcus, Sep 29 2015

More terms from Vincenzo Librandi, Jan 16 2015

cp's OEIS Frontend

A217083 Numbers n such that (n^67-1)/(n-1) is prime.

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A217084 Numbers n such that (n^71-1)/(n-1) is prime.

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A217085 Numbers n such that (n^73-1)/(n-1) is prime.

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A217086 Numbers n such that (n^79-1)/(n-1) is prime.

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A217087 Numbers n such that (n^83-1)/(n-1) is prime.

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A250177 Numbers n such that Phi_21(n) is prime, where Phi is the cyclotomic polynomial.

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A240693 Primes p such that p^10 + p^9 + p^8 + p^7 + p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 is prime.

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A286301 Primes of the form p^10 + p^9 + p^8 + p^7 + p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime.

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