%I #55 Sep 08 2022 08:46:13
%S 11,26,31,205,307,6875,33161
%N Numbers n such that (2^(2n+7) * 5^(2n+5) + 740711) / 33 is prime (n > 0).
%C The numbers that follow the expression in the definition have this form: (12) concatenated n times and prepended to 34567.
%C Empirical observations: primes alternate with nonprimes. 6th (nonprime) and 7th (prime) terms correspond to probable primes. Up to which term the pattern will hold?
%C (2^(2*a(n)+7) * 5^(2*a(n)+5) + 740711) has 7 proper divisors.
%e 11 appears because 121212121212121212121234567 ('12' concatenated 11 times and prepended to '34567') is prime.
%p A260903:=n->`if`(isprime((2^(2*n+7) * 5^(2*n+5) + 740711)/33),n,NULL): seq(A260903(n), n=1..500); # _Wesley Ivan Hurt_, Nov 27 2015
%t Select[Range[500], PrimeQ[(2^(2# + 7) * 5^(2# + 5) + 740711)/33] &] (* or *)
%t Select[Range[50], DivisorSigma[0, (2^(2# + 7) * 5^(2# + 5) + 740711)] - 1 == 7 &] (* inefficient *)
%o (Magma) [n: n in [1..250] | IsPrime((2^(2*n+7) * 5^(2*n+5) + 740711) div 33)]; // _Vincenzo Librandi_, Nov 18 2015
%o (PARI) is(n)=isprime((2^(2*n+7)*5^(2*n+5) + 740711)/33) \\ _Anders Hellström_, Nov 18 2015
%K nonn,base,hard,more
%O 1,1
%A _Mikk Heidemaa_, Nov 17 2015