A252353 Numbers k such that Phi(k, 12) is prime, where Phi is the cyclotomic polynomial.

1, 2, 3, 5, 10, 12, 19, 21, 22, 56, 60, 63, 70, 80, 84, 92, 97, 109, 111, 123, 164, 189, 218, 276, 317, 353, 364, 386, 405, 456, 511, 636, 675, 701, 793, 945, 1090, 1268, 1272, 1971, 2088, 2368, 2482, 2893, 2966, 3290, 4161, 4320, 4533, 4744, 6357, 7023, 7430, 7737, 9499, 9739

Offset: 1

Author

Eric Chen, Dec 16 2014

Keywords

• nonn

Comments

Numbers k such that A019330(k) is prime.

With some exceptions, terms of sequence are such that 12^n - 1 has only one primitive prime factor. 20 is an instance of such an exception, since 12^20 - 1 has a single primitive prime factor, 85403261, but Phi(20, 12) is divisible by 5, it is not prime.

a(n) is a duodecimal unique period length.

Examples

			n         Phi(n, 12)
1         11
2         13
3         157
4         5 * 29
5         22621
6         7 * 19
7         659 * 4943
8         89 * 233
9         37 * 80749
10        19141
11        11 * 23 * 266981089
12        20593
etc.
		

Crossrefs

Cf. A019330, A072226, A138919-A138940.

Programs

Mathematica

Select[Range[1728], PrimeQ[Cyclotomic[#, 12]] &]

PARI

for( i=1, 1728, ispseudoprime( polcyclo(i, 12)) && print1( i", "))

Extensions

More terms from Michel Marcus, Dec 18 2014

More terms from Amiram Eldar, Mar 26 2021