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A070025 At these values of n, the 1st, 2nd, 3rd and 4th cyclotomic polynomials all give prime numbers. 4
6, 150, 2730, 9000, 9240, 35280, 41760, 43050, 53280, 65520, 76650, 96180, 111030, 148200, 197370, 207480, 213360, 226380, 254280, 264600, 309480, 332160, 342450, 352740, 375450, 381990, 440550, 458790, 501030, 527070, 552030, 642360, 660810 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..33.

FORMULA

n-1, n+1, 1+n+n^2 and 1+n^2 are all primes.

EXAMPLE

For n = 6: 5, 7, 43 and 37 are prime values of the first 4 cyclotomic polynomials.

MATHEMATICA

lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1]&&PrimeQ[1+n+n^2]&&PrimeQ[1+n^2], AppendTo[lst, n]], {n, 10^6}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 19 2008 *)

Select[Range[10^6], Function[k, AllTrue[Cyclotomic[#, k] & /@ Range@ 4, PrimeQ]]] (* Michael De Vlieger, Jul 18 2017 *)

CROSSREFS

Cf. A070155, A070156, A070157, A000068, A006313, A006314, A006315, A006316, A056993, A056994, A056995, A005574, A057465, A057002, A070020, A070042.

Sequence in context: A089480 A056427 A056418 * A291110 A246214 A065946

Adjacent sequences:  A070022 A070023 A070024 * A070026 A070027 A070028

KEYWORD

easy,nonn

AUTHOR

Labos Elemer, May 07 2002

STATUS

approved

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Last modified August 26 05:23 EDT 2019. Contains 326328 sequences. (Running on oeis4.)