A193109 Least k such that 2^x + k produces primes for x=1..n and composite for x=n+1.

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

Offset: 1

Author

Arkadiusz Wesolowski, Jul 21 2011

Keywords

• nonn
• more

Comments

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

a(10) was found in 2005 by T. D. Noe and a(11) was found in the same year by Don Reble.

Other known values: a(13) = 29503289812425.

a(12) > 10^13. - Tyler Busby, Feb 19 2023

Crossrefs

Another version of A110096.

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

Programs

Mathematica

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 *)

PARI

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