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Numbers k such that 4^k - 3^k + 2^k is prime.
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%I #33 Nov 21 2024 20:17:46

%S 1,2,4,18,56,60,88,1288,1784,3406,9250,11968,36216,57206,89148

%N Numbers k such that 4^k - 3^k + 2^k is prime.

%C 1 is the only odd number in this sequence.

%C a(15) > 65432.

%C a(16) > 10^5. - _Michael S. Branicky_, Nov 21 2024

%e 4^2 - 3^2 + 2^2 = 16 - 9 + 4 = 11 is prime.

%t Select[Range[0, 5000], PrimeQ[4^# - 3^# + 2^#] &]

%o (PARI) for(n=1, 5000, if(ispseudoprime(4^n-3^n+2^n), print1(n, ", ")))

%Y Cf. A083324, A138699.

%K nonn,more

%O 1,2

%A _Jinyuan Wang_, Aug 09 2018

%E a(13)-a(14) from _Giovanni Resta_, Aug 10 2018

%E a(15) from _Michael S. Branicky_, Nov 21 2024