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%I #24 Sep 08 2022 08:46:14
%S 1,5,155,353,1144,4297,11921,14027
%N Numbers n such that (2^(n+3) * 5^(n+4) - 1463)/9 is prime (n > 0).
%C Numbers n such that '393' appended to n times the digit 5 is prime.
%C Up to a(7) nonprimes alternate with primes; a(9) > 30000 (if it exists).
%e 1 appears because 5393 is prime.
%e 5 appears because 55555393 ('5' concatenated 5 times and prepended to '393') is prime.
%p A265123:=n->`if`(isprime((2^(n+3) * 5^(n+4) - 1463)/9), n, NULL): seq(A265123(n), n=1..1500);
%t Select[Range[1500], PrimeQ[(2^(# + 3) * 5^(# + 4) - 1463) / 9] &]
%o (Magma) [n: n in [1..400] | IsPrime((2^(n+3) * 5^(n+4) - 1463) div 9)];
%o (PARI) is(n)=isprime((2^(n+3)*5^(n+4) - 1463)/9)
%Y Cf. A260903.
%K nonn,base,hard,more
%O 1,2
%A _Mikk Heidemaa_, Dec 02 2015