A259257 -id:A259257 - cp's OEIS frontend

A246392 Numbers n such that Phi(10, n) is prime, where Phi is the cyclotomic polynomial.

2, 3, 5, 10, 11, 12, 16, 20, 21, 22, 33, 37, 38, 43, 47, 48, 55, 71, 75, 76, 80, 81, 111, 121, 126, 131, 133, 135, 136, 141, 155, 157, 158, 165, 176, 177, 180, 203, 223, 242, 245, 251, 253, 256, 257, 258, 265, 268, 276, 286, 290, 297, 307, 322, 323, 342, 361, 363, 366, 375, 377, 385, 388, 396, 411

Offset: 1

Eric Chen, Nov 13 2014

nonn

Numbers n such that (n^5+1)/(n+1) is prime, or numbers n such that A060884(n) is prime.

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 893 terms from Robert Price)
OEIS Wiki, Cyclotomic Polynomials at x=sigma(n)

Cf. A008864 (1), A006093 (2), A002384 (3), A005574 (4), A049409 (5), A055494 (6), A100330 (7), A000068 (8), A153439 (9), this sequence (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).

Cf. A060884, A085398, A259257.

[n: n in [1..500]| IsPrime((n^5+1) div (n+1))]; // Vincenzo Librandi, Nov 14 2014

A246392:=n->`if`(isprime((n^5+1)/(n+1)),n,NULL): seq(A246392(n), n=1..500); # Wesley Ivan Hurt, Nov 15 2014

Select[Range[700], PrimeQ[(#^5 + 1) / (# + 1)] &] (* Vincenzo Librandi, Nov 14 2014 *)

for(n=1,10^3,if(isprime(polcyclo(10,n)),print1(n,", "))); \\ Joerg Arndt, Nov 13 2014

A060884 a(n) = n^4 - n^3 + n^2 - n + 1.

Original entry on oeis.org

1, 1, 11, 61, 205, 521, 1111, 2101, 3641, 5905, 9091, 13421, 19141, 26521, 35855, 47461, 61681, 78881, 99451, 123805, 152381, 185641, 224071, 268181, 318505, 375601, 440051, 512461, 593461, 683705, 783871, 894661, 1016801, 1151041, 1298155, 1458941, 1634221

Offset: 0

N. J. A. Sloane, May 05 2001

a(n) = Phi_10(n), where Phi_k is the k-th cyclotomic polynomial.
Number of walks of length 5 between any two distinct nodes of the complete graph K_{n+1} (n>=1). Example: a(1)=1 because in the complete graph AB we have only one walk of length 5 between A and B: ABABAB. - Emeric Deutsch, Apr 01 2004
t^4-t^3+t^2-t+1 is the Alexander polynomial (with negative powers cleared) of the cinquefoil knot (torus knot T(5,2)). The associated Seifert matrix S is [[ -1, -1, 0, -1], [ 0, -1, 0, 0], [ -1, -1, -1, -1], [ 0, -1, 0, -1]]. a(n) = det(transpose(S)-n*S). Cf. A084849. - Peter Bala, Mar 14 2012
For odd n, a(n) * (n+1) / 2 also represents the first integer in a sum of n^5 consecutive integers that equals n^10. - Patrick J. McNab, Dec 26 2016

Ray Chandler, Table of n, a(n) for n = 0..10000 (first 1001 terms from Harry J. Smith)
Index to values of cyclotomic polynomials of integer argument
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A084849, A246392, A259257.

A060884 := proc(n)
        numtheory[cyclotomic](10,n) ;
end proc:
seq(A060884(n),n=0..20) ; # R. J. Mathar, Feb 07 2014

Table[1 + Fold[(-1)^(#2)*n^(#2) + #1 &, Range[0, 4]], {n, 0, 33}] (* or *)
CoefficientList[Series[(1 - 4 x + 16 x^2 + 6 x^3 + 5 x^4)/(1 - x)^5, {x, 0, 33}], x] (* Michael De Vlieger, Dec 26 2016 *)
Table[n^4-n^3+n^2-n+1,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,1,11,61,205},40] (* Harvey P. Dale, Sep 08 2018 *)

a(n) = { n^4 - n^3 + n^2 - n + 1 } \\ Harry J. Smith, Jul 13 2009

G.f.: (1-4*x+16*x^2+6*x^3+5*x^4)/(1-x)^5. - Emeric Deutsch, Apr 01 2004

E.g.f.: exp(x)*(1 + 5*x^2 + 5*x^3 + x^4). - Stefano Spezia, Apr 22 2023

cp's OEIS Frontend

A246392 Numbers n such that Phi(10, n) is prime, where Phi is the cyclotomic polynomial.

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