A246392 - OEIS

%I #32 Sep 08 2022 08:46:09

%S 2,3,5,10,11,12,16,20,21,22,33,37,38,43,47,48,55,71,75,76,80,81,111,

%T 121,126,131,133,135,136,141,155,157,158,165,176,177,180,203,223,242,

%U 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

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

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

%H Ray Chandler, <a href="/A246392/b246392.txt">Table of n, a(n) for n = 1..10000</a> (first 893 terms from Robert Price)

%H OEIS Wiki, <a href="https://oeis.org/wiki/Cyclotomic Polynomials at x=sigma(n)">Cyclotomic Polynomials at x=sigma(n)</a>

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

%t Select[Range[700], PrimeQ[(#^5 + 1) / (# + 1)] &] (* _Vincenzo Librandi_, Nov 14 2014 *)

%o (PARI) for(n=1,10^3,if(isprime(polcyclo(10,n)),print1(n,", "))); \\ _Joerg Arndt_, Nov 13 2014

%o (Magma) [n: n in [1..500]| IsPrime((n^5+1) div (n+1))]; // _Vincenzo Librandi_, Nov 14 2014

%Y 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).

%Y Cf. A060884, A085398, A259257.

%K nonn

%O 1,1

%A _Eric Chen_, Nov 13 2014