A070025 - OEIS

A070025

At these values of k, the 1st, 2nd, 3rd and 4th cyclotomic polynomials all give prime numbers.

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

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OFFSET

1,1

COMMENTS

Numbers k such that k-1, k+1, k^2+k+1 and k^2+1 are all primes.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

For k = 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 *)

PROG

(PARI) is(k) = isprime(k-1) && isprime(k+1) && isprime(k^2+1) && isprime(k^2+k+1); \\ Amiram Eldar, Sep 24 2024

CROSSREFS

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

Sequence in context: A056427 A056418 A346694 * A291110 A246214 A065946

Adjacent sequences: A070022 A070023 A070024 * A070026 A070027 A070028

KEYWORD

easy,nonn

AUTHOR

Labos Elemer, May 07 2002

STATUS

approved