A193109 - OEIS

%I #44 Feb 19 2023 04:09:30

%S 0,1,9,3,225,15,65835,1605,19425,2397347205,153535525935

%N Least k such that 2^x + k produces primes for x=1..n and composite for x=n+1.

%C All terms except the first four are congruent to 15 mod 30.

%C a(10) was found in 2005 by _T. D. Noe_ and a(11) was found in the same year by _Don Reble_.

%C Other known values: a(13) = 29503289812425.

%C a(12) > 10^13. - _Tyler Busby_, Feb 19 2023

%t Table[k = 0; While[i = 1; While[i <= n && PrimeQ[2^i + k], i++]; i <= n || PrimeQ[2^i + k], k++]; k, {n, 9}] (* _T. D. Noe_, Jul 21 2011 *)

%o (PARI) is(k, n) = for(x=1, n, if(!isprime(k+2^x), return(0))); 1;

%o a(n) = {my(s=2); forprime(p=3, n, if(znorder(Mod(2, p))==(p-1), s*=p)); forstep(k=s*(n>1)/2, oo, s, if(is(k, n) && !isprime(k+2^(n+1)), return(k))); } \\ _Jinyuan Wang_, Jul 30 2020

%Y Another version of A110096.

%Y Cf. A008597, A057733, A092506, A104070, A144487.

%K nonn,more

%O 1,3

%A _Arkadiusz Wesolowski_, Jul 21 2011