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%I #52 Jun 01 2024 08:45:13
%S 1,2,3,4,5,8,9,15,18,23,24,33,34,35,44,63,88,89,120,220,228,229,570,
%T 1095,1863,2094,2718,3598,4658,6056,8819,9485,11220,23656,28762,35664,
%U 36544,39779,46868,50098,58853
%N Numbers k such that 2^k + 3^k + 6 is prime.
%C a(34) > 17000.
%C a(36) > 30000. - _Jon E. Schoenfield_, Jun 14 2022
%e For k=1 we obtain f(1) = 2^1 + 3^1 + 6 = 11 which is a prime.
%t Select[Range[1, 1000], PrimeQ[2^# + 3^# + 6] &]
%o (Python)
%o from sympy import isprime
%o from itertools import count, islice
%o def agen(): yield from (k for k in count(1) if isprime(2**k+3**k+6))
%o print(list(islice(agen(), 24))) # _Michael S. Branicky_, Jun 07 2022
%Y Cf. A353102.
%K nonn,more,hard
%O 1,2
%A _Hemjyoti Nath_, Jun 07 2022
%E a(34) from _Jon E. Schoenfield_, Jun 11 2022
%E a(35) from _Jon E. Schoenfield_, Jun 13 2022
%E a(36)-a(38) from _Michael S. Branicky_, Mar 14 2023
%E a(39)-a(41) from _Michael S. Branicky_, Jun 01 2024