A060885 -id:A060885 - cp's OEIS frontend

A162862 Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime.

1, 5, 17, 20, 21, 30, 53, 60, 86, 137, 172, 195, 212, 224, 229, 258, 268, 272, 319, 339, 355, 365, 366, 389, 390, 398, 414, 467, 480, 504, 534, 539, 543, 567, 592, 619, 626, 654, 709, 735, 756, 766, 770, 778, 787, 806, 812, 874, 943, 973, 1003, 1036, 1040

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 14 2009

nonn

The associated primes are in A162861.

Numbers n such that Phi(11,n) is prime, where Phi(11,n) = (n^11 - 1)/(n - 1) is the eleventh cyclotomic polynomial. - Jianing Song, Sep 05 2018

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index to values of cyclotomic polynomials of integer argument

Cf. A060885, A162861.

Select[Range[100], PrimeQ[1 + Sum[#^i, {i, 10}]] &] (* Alonso del Arte, Apr 11 2014 *)

is(n)=isprime(polcyclo(11,n)) \\ Charles R Greathouse IV, Sep 14 2015

A000040 INTERSECT A060885.

A198300 Square array M(k,g), read by antidiagonals, of the Moore lower bound on the order of a (k,g)-cage.

Original entry on oeis.org

3, 4, 4, 5, 6, 5, 6, 8, 10, 6, 7, 10, 17, 14, 7, 8, 12, 26, 26, 22, 8, 9, 14, 37, 42, 53, 30, 9, 10, 16, 50, 62, 106, 80, 46, 10, 11, 18, 65, 86, 187, 170, 161, 62, 11, 12, 20, 82, 114, 302, 312, 426, 242, 94, 12, 13, 22, 101, 146, 457, 518, 937, 682, 485, 126, 13

Offset: 1

Jason Kimberley, Oct 27 2011

k >= 2; g >= 3.
The base k-1 reading of the base 10 string of A094626(g).
Exoo and Jajcay Theorem 1: M(k,g) <= A054760(k,g) with equality if and only if: k = 2 and g >= 3; g = 3 and k >= 2; g = 4 and k >= 2; g = 5 and k = 2, 3, 7 or possibly 57; or g = 6, 8, or 12, and there exists a symmetric generalized n-gon of order k - 1.

			This is the table formed from the antidiagonals for k+g = 5..20:
3   4   5   6    7    8    9     10    11    12    13    14    15   16  17 18
4   6  10  14   22   30    46    62    94   126   190   254   382  510 766
5   8  17  26   53   80   161   242   485   728  1457  2186  4373 6560
6  10  26  42  106  170   426   682  1706  2730  6826 10922 27306
7  12  37  62  187  312   937  1562  4687  7812 23437 39062
8  14  50  86  302  518  1814  3110 10886 18662 65318
9  16  65 114  457  800  3201  5602 22409 39216
10 18  82 146  658 1170  5266  9362 42130
11 20 101 182  911 1640  8201 14762
12 22 122 222 1222 2222 12222
13 24 145 266 1597 2928
14 26 170 314 2042
15 28 197 366
16 30 226
17 32
18

E. Bannai and T. Ito, On finite Moore graphs, J. Fac. Sci. Tokyo, Sect. 1A, 20 (1973) 191-208.
R. M. Damerell, On Moore graphs, Proc. Cambridge Phil. Soc. 74 (1973) 227-236.

Jason Kimberley, Table of n, a(n) for n = 1..20100 (k+g = 5..204)
Jason Kimberley, Table of n, k+g, k, g, M(k,g)=a(n) for k+g = 5..204 (n = 1..20100)
G. Exoo and R. Jajcay, Dynamic cage survey, Electr. J. Combin. (2008, 2011).
Gordon Royle, Cages of higher valency

Moore lower bound on the order of a (k,g) cage: this sequence (square); rows: A000027 (k=2), A027383 (k=3), A062318 (k=4), A061547 (k=5), A198306 (k=6), A198307 (k=7), A198308 (k=8), A198309 (k=9), A198310 (k=10), A094626 (k=11); columns: A020725 (g=3), A005843 (g=4), A002522 (g=5), A051890 (g=6), A188377 (g=7), 2*A053698 (g=8), 2*A053699 (g=10), 2*A053700 (g=12), 2*A053716 (g=14), 2*A053716 (g=16), 2*A102909 (g=18), 2*A103623 (g=20), 2*A060885 (g=22), 2*A105067 (g=24), 2*A060887 (g=26), 2*A104376 (g=28), 2*A104682 (g=30), 2*A105312 (g=32).

Cf. A054760 (the actual order of a (k,g)-cage).

ExtendedStringToInt:=func;
M:=func;
k_:=2;g_:=3;
anti:=func;
[anti(kg):kg in[5..15]];

Table[Function[g, FromDigits[#, k - 1] &@ IntegerDigits@ SeriesCoefficient[x (1 + x)/((1 - x) (1 - 10 x^2)), {x, 0, g}]][n - k + 3], {n, 2, 12}, {k, n, 2, -1}] // Flatten (* Michael De Vlieger, May 15 2017 *)

M(k,2i) = 2 sum_{j=0}^{i-1}(k-1)^j =  string "2"^i read in base k-1.
M(k,2i+1) = (k-1)^i +  2 sum_{j=0}^{i-1}(k-1)^j = string "1"*"2"^i read in base k-1.
Recurrence:
M(k,3) = k + 1,
M(k,2i) = M(k,2i-1) + (k-1)^(i-1),
M(k,2i+1) = M(k,2i) + (k-1)^i.

A269442 a(n) = n(n^8 + 1)(n^4 + 1)(n^2 + 1)(n + 1) + 1.

Original entry on oeis.org

1, 17, 131071, 64570081, 5726623061, 190734863281, 3385331888947, 38771752331201, 321685687669321, 2084647712458321, 11111111111111111, 50544702849929377, 201691918794585181, 720867993281778161, 2345488209948553531, 7037580381120954241

Offset: 0

Ilya Gutkovskiy, Feb 26 2016

a(n) = Phi_17(n) where Phi_k(x) is the k-th cyclotomic polynomial.

G. C. Greubel, Table of n, a(n) for n = 0..1000
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
Index to values of cyclotomic polynomials of integer argument
Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Cf. similar sequences of the type Phi_k(n), where Phi_k is the k-th cyclotomic polynomial: A000012 (k=0), A023443 (k=1), A000027 (k=3), A002522 (k=4), A053699 (k=5), A002061 (k=6), A053716 (k=7), A002523 (k=8), A060883 (k=9), A060884 (k=10), A060885 (k=11), A060886 (k=12), A060887 (k=13), A060888 (k=14), A060889 (k=15), A060890 (k=16), this sequence (k=17), A060891 (k=18), A269446 (k=19).

List([0..20], n-> n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1); # G. C. Greubel, Apr 24 2019

[n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1: n in [0..20]]; // Vincenzo Librandi, Feb 27 2016

Mathematica
```
Table[Cyclotomic[17, n], {n, 0, 15}]
```

a(n)=n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1 \\ Charles R Greathouse IV, Jul 26 2016

[n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1 for n in (0..20)] # G. C. Greubel, Apr 24 2019

G.f.: (1 +130918*x^2 +62343506*x^3 +4646748160*x^4 +102074708252*x^5 +878064150546*x^6 +3419813860214*x^7 +6502752956958*x^8 +6232856389160*x^9 +3004612851498*x^10 +701875014878*x^11 +73106078368*x^12 +2893069436*x^13 +31542430*x^14 +43674*x^15 +x^16)/(1 - x)^17.

Sum_{n>=0} 1/a(n) = 1.05883117453...

A060887 a(n) = Sum_{j=0..12} n^j.

Original entry on oeis.org

1, 13, 8191, 797161, 22369621, 305175781, 2612138803, 16148168401, 78536544841, 317733228541, 1111111111111, 3452271214393, 9726655034461, 25239592216021, 61054982558011, 139013933454241, 300239975158033, 619036127056621, 1224880286215951, 2336276859014281, 4311578947368421

Offset: 0

N. J. A. Sloane, May 05 2001

a(n) = Phi_13(n) where Let Phi_k is the k-th cyclotomic polynomial.

Harry J. Smith, Table of n, a(n) for n = 0..1000
Index to values of cyclotomic polynomials of integer argument
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Cf. A053698, A053699, A053700, A053716, A053717, A102909, A103623, A060885, A102909, A104376, A104682, A105067.

[(&+[n^j: j in [0..12]]): n in [0..20]]; // G. C. Greubel, Apr 14 2019

A060887 := proc(n)
        numtheory[cyclotomic](13,n) ;
end proc:
seq(A060887(n),n=0..20) ; # R. J. Mathar, Feb 11 2014

Table[1 + Sum[n^j, {j, 1, 12}], {n, 0, 20}] (* G. C. Greubel, Apr 14 2019 *)

a(n) = { n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 } \\ Harry J. Smith, Jul 14 2009

A060887(n)=polcyclo(13,n) \\ M. F. Hasler, Dec 31 2012

[sum(n^j for j in (0..12)) for n in (0..20)] # G. C. Greubel, Apr 14 2019

a(n) = n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.
G.f.: (x^12 + 2718*x^11 + 363156*x^10 + 8452952*x^9 + 59276439*x^8 + 155812164*x^7 + 167537592*x^6 + 74214648*x^5 + 12642423*x^4 + 691406*x^3 + 8100*x^2 + 1)/(1-x)^13. - Colin Barker, Oct 29 2012
a(n) = (n^13-1)/(n-1) with a(1) = 13 = lim_{x->1} a(x). - M. F. Hasler, Dec 31 2012

Name changed by G. C. Greubel, Apr 14 2019

A162861 Primes of the form n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.

Original entry on oeis.org

11, 12207031, 2141993519227, 10778947368421, 17513875027111, 610851724137931, 178250690949465223, 614910264406779661, 22390512687494871811, 2346320474383711003267, 22793803793211153712637

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 14 2009

nonn

The corresponding n is given in A162862. This sequence lists primes of the form Phi(11,k), where Phi(11,k) = (k^11 - 1)/(k - 1) is the eleventh cyclotomic polynomial. - Jianing Song, Sep 05 2018

Index to values of cyclotomic polynomials of integer argument

Cf. A060885, A162862.

Select[Table[Total[n^Range[0,10]],{n,200}],PrimeQ] (* Harvey P. Dale, Feb 06 2015 *)

print1(11);for(n=2,1000,k=(n^11-1)/(n-1);if(isprime(k),print1(","k)))

Program by Charles R Greathouse IV, Oct 12 2009

A102909 a(n) = Sum_{j=0..8} n^j.

Original entry on oeis.org

1, 9, 511, 9841, 87381, 488281, 2015539, 6725601, 19173961, 48427561, 111111111, 235794769, 469070941, 883708281, 1589311291, 2745954241, 4581298449, 7411742281, 11668193551, 17927094321, 26947368421, 39714002329, 57489010371, 81870575521, 114861197401

Offset: 0

Douglas Winston (douglas.winston(AT)srupc.com), Mar 01 2005

G. C. Greubel, Table of n, a(n) for n = 0..1000
Carlos M. da Fonseca and Anthony G. Shannon, A formal operator involving Fermatian numbers, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 491-498.
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A001016, A060890, A059839.

Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), this sequence (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), A104376 (m=13), A104682 (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).

[(&+[n^j: j in [0..8]]): n in [0..30]]; // G. C. Greubel, Feb 13 2018

1 + Sum[Range[0, 30]^j, {j, 1, 8}] (* G. C. Greubel, Feb 13 2018 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,9,511,9841,87381,488281,2015539,6725601,19173961},30] (* Harvey P. Dale, Feb 01 2025 *)

a(n)=n^8+n^7+n^6+n^5+n^4+n^3+n^2+n+1 \\ Charles R Greathouse IV, Oct 07 2015

[sum(n^j for j in (0..8)) for n in (0..30)] # G. C. Greubel, Apr 14 2019

a(n) = (n^2+n+1) * (n^6+n^3+1) and so is never prime. - Jonathan Vos Post, Dec 21 2012
G.f.: (x^8 + 162*x^7 + 3418*x^6 + 14212*x^5 + 16578*x^4 + 5482*x^3 + 466*x^2 + 1)/(1-x)^9. - Colin Barker, Nov 05 2012, edited by M. F. Hasler, Dec 31 2012
a(n) = (n^9-1)/(n-1) with a(1) = 9. - L. Edson Jeffery and M. F. Hasler, Dec 30 2012
E.g.f.: exp(x)*(1 + 8*x + 247*x^2 + 1389*x^3 + 2127*x^4 + 1206*x^5 + 288*x^6 + 29*x^7 + x^8). - Stefano Spezia, Oct 03 2024

Offset corrected by N. J. A. Sloane, Dec 30 2012

A104376 a(n) = Sum_{j=0..13} n^j.

Original entry on oeis.org

1, 14, 16383, 2391484, 89478485, 1525878906, 15672832819, 113037178808, 628292358729, 2859599056870, 11111111111111, 37974983358324, 116719860413533, 328114698808274, 854769755812155, 2085209001813616, 4803839602528529, 10523614159962558, 22047845151887119

Offset: 0

Douglas Winston (douglas.winston(AT)srupc.com), Apr 16 2005

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j are: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), A102909 (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), this sequence (m=13), A104682 (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).

[(&+[n^j: j in [0..13]]): n in [0..20]]; // Vincenzo Librandi, May 01 2011

Table[1+Sum[n^j, {j,1,13}], {n,0,20}] (* G. C. Greubel, Apr 14 2019 *)
LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1},{1,14,16383,2391484,89478485,1525878906,15672832819,113037178808,628292358729,2859599056870,11111111111111,37974983358324,116719860413533,328114698808274},20] (* Harvey P. Dale, Sep 04 2023 *)

a(n)=sum(j=0,13, n^j) \\ Charles R Greathouse IV, Oct 07 2015

[sum(n^j for j in (0..13)) for n in (0..20)] # G. C. Greubel, Apr 14 2019

a(n) = n^13 + n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n^1 + 1.

G.f.: (5461*x^12 + 1119288*x^11 + 37443654*x^10 + 372458048*x^9 + 1409085783*x^8 + 2263446576*x^7 + 1598944452*x^6 + 484853760*x^5 + 57484467*x^4 + 2163032*x^3 + 16278*x^2 + 1)/(1-x)^14. - Colin Barker, Nov 04 2012

Name changed by G. C. Greubel, Apr 14 2019

A104682 a(n) = Sum_{j=0..14} n^j.

Original entry on oeis.org

1, 15, 32767, 7174453, 357913941, 7629394531, 94036996915, 791260251657, 5026338869833, 25736391511831, 111111111111111, 417724816941565, 1400638324962397, 4265491084507563, 11966776581370171, 31278135027204241, 76861433640456465, 178901440719363487

Offset: 0

Douglas Winston (douglas.winston(AT)srupc.com), Apr 22 2005

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j are: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), A102909 (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), A104376 (m=13), this sequence (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).

[(&+[n^j: j in [0..14]]): n in [0..20]]; // Vincenzo Librandi, May 01 2011

With[{f=Total[n^Range[0,14]]},Table[f,{n,0,20}]] (* Harvey P. Dale, Jun 11 2011 *)

a(n) = sum(j=0, 14, n^j) \\ Charles R Greathouse IV, Oct 07 2015

[sum(n^j for j in (0..14)) for n in (0..20)] # G. C. Greubel, Apr 15 2019

a(n) = n^14 + n^13 + n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n^1 + 1.
a(n) = (n^2 + n + 1) * (n^4 + n^3 + n^2 + n + 1) * (n^8 - n^7 + n^5 - n^4 + n^3 - n + 1). - Jonathan Vos Post, Apr 23 2005
G.f.: (x^14 +10908*x^13 +3423487*x^12 +162086420*x^11 +2236727781*x^10 +11806635128*x^9 +27116815299*x^8 +28635678216*x^7 +13957353555*x^6 +2999111468*x^5 +253732221*x^4 +6684068*x^3 +32647*x^2 +1)/(1-x)^15. - Colin Barker, Nov 04 2012

More terms from Harvey P. Dale, Jun 11 2011

Name changed by G. C. Greubel, Apr 15 2019

A105067 a(n) = Sum_{j=0..11} n^j.

Original entry on oeis.org

1, 12, 4095, 265720, 5592405, 61035156, 435356467, 2306881200, 9817068105, 35303692060, 111111111111, 313842837672, 810554586205, 1941507093540, 4361070182715, 9267595563616, 18764998447377, 36413889826860

Offset: 0

Douglas Winston (douglas.winston(AT)srupc.com), Apr 05 2005

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), A102909 (m=8), A103623 (m=9), A060885 (m=10), this sequence (m=11), A060887 (m=12), A104376 (m=13), A104682 (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).

[n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1: n in [0..20]]; // Vincenzo Librandi, May 01 2011

1+Sum[Range[0,20]^j, {j,1,11}] (* G. C. Greubel, Apr 13 2019 *)

a(n)=polcyclo(11,n)+n^11 \\ Charles R Greathouse IV, Sep 03 2011

[sum(n^j for j in (0..11)) for n in (0..20)] # G. C. Greubel, Apr 13 2019

Factorization of the polynomial into irreducible components over integers: n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 = +- (n + 1) * (n^2 - n + 1) * (n^2 + 1) * (n^2 + n + 1) * (n^4 - n^2 + 1). - Jonathan Vos Post, Apr 06 2005

G.f.: (1365*x^10 + 116480*x^9 + 1851213*x^8 + 8893248*x^7 + 15593370*x^6 + 10568064*x^5 + 2671890*x^4 + 217152*x^3 + 4017*x^2 + 1)/(x - 1)^12. - Colin Barker, Oct 29 2012

Signature changed by Georg Fischer, Apr 13 2019

A105312 a(n) = Sum_{j=0..15} n^j.

Original entry on oeis.org

1, 16, 65535, 21523360, 1431655765, 38146972656, 564221981491, 5538821761600, 40210710958665, 231627523606480, 1111111111111111, 4594972986357216, 16807659899548765, 55451384098598320, 167534872139182395, 469172025408063616, 1229782938247303441

Offset: 0

Douglas Winston (douglas.winston(AT)srupc.com), Apr 30 2005

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j are: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), A102909 (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), A104376 (m=13), A104682 (m=14), this sequence (m=15), A269442 (m=16), A269446 (m=18).

[(&+[n^j: j in [0..15]]): n in [0..20]]; // Vincenzo Librandi, May 01 2011 (modified by G. C. Greubel, Apr 14 2019)

a:= n-> add(n^k, k=0..15):
seq(a(n), n=0..20);  # Alois P. Heinz, Nov 04 2012

Prepend[Table[Total[n^Range[0,15]],{n,20}],1]  (* Harvey P. Dale, Jan 19 2011 *)

vector(20, n, n--; sum(j=0,15, n^j)) \\ G. C. Greubel, Apr 14 2019

[sum(n^j for j in (0..15)) for n in (0..20)] # G. C. Greubel, Apr 14 2019

a(n) = n^15 + n^14 + n^13 + n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n^1 + 1.

G.f.: (21845*x^14 + 10412160*x^13 + 689427979*x^12 + 12966588160*x^11 + 93207091581*x^10 + 296077418240*x^9 + 446019954555*x^8 + 326065923072*x^7 + 113735241015*x^6 + 17786608768*x^5 + 1095139065*x^4 + 20476160*x^3 + 65399*x^2 +1 )/(x-1)^16. - Colin Barker, Nov 04 2012

More terms from Harvey P. Dale, Jan 19 2011

Name changed by G. C. Greubel, Apr 14 2019

cp's OEIS Frontend

A162862 Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime.

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A198300 Square array M(k,g), read by antidiagonals, of the Moore lower bound on the order of a (k,g)-cage.

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A269442 a(n) = n*(n^8 + 1)*(n^4 + 1)*(n^2 + 1)*(n + 1) + 1.

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A060887 a(n) = Sum_{j=0..12} n^j.

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A162861 Primes of the form n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.

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A102909 a(n) = Sum_{j=0..8} n^j.

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A104376 a(n) = Sum_{j=0..13} n^j.

A269442 a(n) = n(n^8 + 1)(n^4 + 1)(n^2 + 1)(n + 1) + 1.