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URL: https://oeis.org/A252353

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A252353
Numbers k such that Phi(k, 12) is prime, where Phi is the cyclotomic polynomial.
0
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
1,2
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.
EXAMPLE
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.
MATHEMATICA
Select[Range[1728], PrimeQ[Cyclotomic[#, 12]] &]
PROG
(PARI) for( i=1, 1728, ispseudoprime( polcyclo(i, 12)) && print1( i", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Chen, Dec 16 2014
EXTENSIONS
More terms from Michel Marcus, Dec 18 2014
More terms from Amiram Eldar, Mar 26 2021
STATUS
approved