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

%I A252353 #42 Mar 26 2021 08:38:50
%S A252353 1,2,3,5,10,12,19,21,22,56,60,63,70,80,84,92,97,109,111,123,164,189,
%T A252353 218,276,317,353,364,386,405,456,511,636,675,701,793,945,1090,1268,
%U A252353 1272,1971,2088,2368,2482,2893,2966,3290,4161,4320,4533,4744,6357,7023,7430,7737,9499,9739
%N A252353 Numbers k such that Phi(k, 12) is prime, where Phi is the cyclotomic polynomial.
%C A252353 Numbers k such that A019330(k) is prime.
%C A252353 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.
%C A252353 a(n) is a duodecimal unique period length.
%e A252353 n         Phi(n, 12)
%e A252353 1         11
%e A252353 2         13
%e A252353 3         157
%e A252353 4         5 * 29
%e A252353 5         22621
%e A252353 6         7 * 19
%e A252353 7         659 * 4943
%e A252353 8         89 * 233
%e A252353 9         37 * 80749
%e A252353 10        19141
%e A252353 11        11 * 23 * 266981089
%e A252353 12        20593
%e A252353 etc.
%t A252353 Select[Range[1728], PrimeQ[Cyclotomic[#, 12]] &]
%o A252353 (PARI) for( i=1, 1728, ispseudoprime( polcyclo(i, 12)) && print1( i", "))
%Y A252353 Cf. A019330, A072226, A138919-A138940.
%K A252353 nonn
%O A252353 1,2
%A A252353 _Eric Chen_, Dec 16 2014
%E A252353 More terms from _Michel Marcus_, Dec 18 2014
%E A252353 More terms from _Amiram Eldar_, Mar 26 2021