A100330 -id:A100330 - cp's OEIS frontend

A217081 Numbers n such that (n^59-1)/(n-1) is prime.

19, 70, 102, 116, 126, 188, 209, 257, 294, 359, 451, 461, 468, 470, 638, 653, 710, 762, 766, 781, 824, 901, 939, 964, 995, 1036, 1047, 1098, 1150, 1211, 1234, 1243, 1256, 1278, 1389, 1401, 1422, 1436, 1454, 1492, 1523, 1639, 1703, 1705, 1826, 1913, 1915, 1978

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.

[n: n in [2..2000] |IsPrime((n^59 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 2000], PrimeQ[(#^59 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^59-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

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

A217082 Numbers n such that (n^61-1)/(n-1) is prime.

Original entry on oeis.org

2, 19, 69, 88, 138, 155, 205, 234, 336, 420, 425, 455, 470, 525, 555, 561, 608, 626, 667, 674, 766, 779, 846, 851, 937, 971, 998, 1053, 1055, 1112, 1137, 1263, 1329, 1383, 1445, 1448, 1499, 1544, 1551, 1578, 1640, 1689, 1724, 1750, 1793, 1868, 2143, 2241, 2358

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.

[n: n in [2..2400] |IsPrime((n^61 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 2400], PrimeQ[(#^61 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^61-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

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

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

Original entry on oeis.org

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

A163268 Primes p such that 1 + p + p^2 + p^3 + p^4 + p^5 + p^6 is prime.

Original entry on oeis.org

2, 3, 5, 13, 17, 31, 61, 73, 89, 149, 163, 251, 349, 353, 461, 523, 599, 647, 863, 941, 947, 1087, 1117, 1229, 1277, 1291, 1297, 1409, 1439, 1489, 1567, 1579, 1609, 1627, 1753, 1783, 1831, 2039, 2131, 2293, 2531, 2609, 2753, 2861, 3037, 3163, 3167, 3299

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 24 2009

nonn

Primes in A100330. The generated prime numbers are exactly A194257. [Bernard Schott, Dec 21 2012]

Robert Israel, Table of n, a(n) for n = 1..10000 (first 102 terms from Zak Seidov)

Cf. A053182, A065509, A088550, A100330, A163268, A194257.

select(p -> isprime(p) and isprime(1+p+p^2+p^3+p^4+p^5+p^6), [2,seq(i,i=3..10000,2)]); # Robert Israel, May 05 2017

f[n_]:=1+n+n^2+n^3+n^4+n^5+n^6; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst,p]], {n,7!}]; lst
Select[Prime[Range[500]],PrimeQ[Total[#^Range[0,6]]]&] (* Harvey P. Dale, Jul 13 2022 *)

n=0;forprime(p=2,10000,isprime((p^7-1)/(p-1))&&print(n++" "p))\\ Zak Seidov, Mar 09 2013

Edited (but not checked) by N. J. A. Sloane, Jul 25 2009

A100331 Positive integers n such that n^6 + n^5 + n^4 + n^3 + n^2 + n - 1 is prime.

Original entry on oeis.org

1, 3, 9, 15, 18, 20, 28, 33, 55, 65, 68, 84, 88, 98, 109, 115, 119, 120, 124, 129, 134, 135, 140, 159, 165, 173, 185, 188, 190, 205, 223, 239, 264, 270, 275, 278, 288, 295, 305, 308, 323, 329, 350, 368, 370, 388, 409, 460, 464, 499, 510, 525, 540, 565, 579, 593

Offset: 1

Ray G. Opao, Nov 16 2004

			3 is in the sequence because 3^6 + 3^5 + 3^4 + 3^3 + 3^2 + 3 - 1 = 1091, which is prime.

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

Cf. A100330.

[n: n in [0..700] | IsPrime(n^6+n^5+n^4+n^3+n^2+n-1)]; // Vincenzo Librandi, Dec 13 2015

A100331:=n->`if`(isprime(-1+add(n^i, i=1..6)), n, NULL): seq(A100331(n), n=1..1000); # Wesley Ivan Hurt, Dec 13 2015

Select[Range[600], PrimeQ[Sum[ #^i, {i, 6}] - 1] &] (* Ray Chandler, Nov 17 2004 *)

is(n) = ispseudoprime(n^6+n^5+n^4+n^3+n^2+n-1) \\ Altug Alkan, Dec 13 2015

cp's OEIS Frontend

A217081 Numbers n such that (n^59-1)/(n-1) is prime.

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A217082 Numbers n such that (n^61-1)/(n-1) is prime.

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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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Extensions

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

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