A110096 -id:A110096 - cp's OEIS frontend

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

Arkadiusz Wesolowski, Jul 21 2011

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

Another version of A110096.

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

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 *)

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

A130003 a(n) is the smallest positive integer m such that 4^k + m is prime for all k=1,2,...,n.

Original entry on oeis.org

1, 1, 3, 7, 7, 15, 37, 163, 177, 4503, 4503, 4503, 4503, 4503, 833021343, 12465115083, 95854279610863, 1158174141556287

Offset: 1

Farideh Firoozbakht, May 30 2007, Jun 04 2007

			a(14)=4503 because 4^k + 4503 is prime for each k in 1..14 and there is no smaller number with this property.

Carlos Rivera, Puzzle 403. 833021343, The Prime Puzzles and Problems Connection.

Cf. A110096.

More terms from Jens Kruse Andersen, Jun 08 2007

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

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A130003 a(n) is the smallest positive integer m such that 4^k + m is prime for all k=1,2,...,n.

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