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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 (list; graph; refs; listen; history; text; internal format)
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, A138919-A138940.

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

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Last modified March 25 20:38 EDT 2019. Contains 321477 sequences. (Running on oeis4.)