A070042 At these values of k the 1st, 2nd, 3rd, 4th and 5th cyclotomic polynomials all give prime numbers.

1068630, 1441590, 1867950, 3429300, 4084230, 5651730, 6322890, 6770610, 7158630, 7804830, 9437760, 9624270, 13625850, 23194860, 25848840, 26588520, 28714950, 29451840, 32984430, 33650580, 36500910, 38177130, 42856590, 49531020, 50016540, 50222070, 52083330, 54637590

Offset

1,1

Comments

Numbers k such that C1(k) = k-1, C2(k) = k+1, C3(k) = k^2+k+1, C4(k) = k^2+1 and C5(k) = k^4+k^3+k^2+k+1 are all primes.

Links

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

Example

For k = 1068630: the 1st, 2nd, 3rd, 4th and 5th cyclotomic polynomials give a quintet of primes: {1068629, 1068631, 1141971145531, 1141970076901, 1304096876879617162402531}.

Prog

(PARI) is(k) = isprime(k-1) && isprime(k+1) && isprime(k^2+1) && isprime(k^2+k+1) && isprime(k^4+k^3+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, A070025.

Sequence in context: A193054 A160687 A342328 * A258061 A187125 A237972

Adjacent sequences: A070039 A070040 A070041 * A070043 A070044 A070045

Keyword

easy,nonn

Author

Labos Elemer, May 07 2002

Extensions

More terms from Don Reble, May 11 2002

a(24)-a(28) from Amiram Eldar, Sep 24 2024

Status

approved