

A252353


Numbers n such that Phi(n, 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
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OFFSET

1,2


COMMENTS

Numbers n such that A019330(n) 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.


LINKS

Table of n, a(n) for n=1..45.


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

Cf. A072226, A138919A138940.
Sequence in context: A079251 A171785 A050051 * A241167 A083571 A123090
Adjacent sequences: A252350 A252351 A252352 * A252354 A252355 A252356


KEYWORD

nonn


AUTHOR

Eric Chen, Dec 16 2014


EXTENSIONS

More terms from Michel Marcus, Dec 18 2014


STATUS

approved



