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%I #15 Apr 14 2023 13:52:38
%S 1,3,4,9,11,69,117,449,675,1119,1959,2687,2859,8001,8175,24269
%N Integers k such that (2^k - 1) + (3^k - 1) + (5^k - 1) is prime.
%C Inspired by A268067.
%C Corresponding primes are 7, 157, 719, 1973317, 49007317, ...
%e 4 is a term because (2^4 - 1) + (3^4 - 1) + (5^4 - 1) = 719 is a prime number.
%t Select[Range@ 3000, PrimeQ[(2^# - 1) + (3^# - 1) + (5^# - 1)] &] (* _Michael De Vlieger_, Mar 23 2016 *)
%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(-3 + 2^n + 3^n + 5^n), print1(n, ", ")));
%o (Python)
%o from sympy import isprime
%o def afind(limit, startk=1):
%o pow2, pow3, pow5 = 2**startk, 3**startk, 5**startk
%o for k in range(startk, limit+1):
%o if isprime(pow2 + pow3 + pow5 - 3): print(k, end=", ")
%o pow2 *= 2; pow3 *= 3; pow5 *= 5
%o afind(1200) # _Michael S. Branicky_, Sep 08 2021
%Y Cf. A268064, A268067.
%K nonn,more
%O 1,2
%A _Altug Alkan_, Mar 23 2016
%E a(14)-a(15) from _Michael S. Branicky_, Sep 08 2021
%E a(16) from _Michael S. Branicky_, Apr 13 2023
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