A289154 Smallest prime p > 2^n such that none of p -+ 2^0, p -+ 2^1, p -+ 2^2, ..., p -+ 2^n are prime.

5, 23, 53, 211, 251, 787, 787, 1409, 1777, 1777, 1973, 3181, 4889, 8363, 19583, 34171, 66683, 131701, 263227, 527099, 1049011, 2098027, 4196407, 8389001, 16779001, 33555517, 67108913, 134219273, 268435537, 536871743, 1073743303, 2147485673, 4294968857

Offset: 0

Author

Juri-Stepan Gerasimov, Jun 26 2017

Keywords

• nonn

Examples

			a(0) = 5 because prime 5 > 2^0 = 1 and none of 5 - 2^0 = 4, 5 + 2^0 = 6 are prime,
a(1) = 23 because prime 23 > 2^1 = 2 and none of 23 - 2^2 = 22, 23 + 2^0 = 24, 23 - 2^1 = 21, 23 + 2^1 = 25 are prime,
a(2) = 53 because prime 53 > 2^2 = 4 and none of 53 - 2^0 = 52, 53 + 2^0 = 54, 53 - 2^1 = 51, 53 + 2^1 = 55, 53 - 2^2 = 49, 53 + 2^2 = 57 are prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A120937.

Programs

Mathematica

Table[p = NextPrime[2^n]; While[AnyTrue[p + Flatten@ Map[2^Range[0, n] # &, {-1, 1}], PrimeQ], p = NextPrime@ p]; p, {n, 0, 32}] (* Michael De Vlieger, Jun 27 2017 *)

PARI

a(n)=if(n<1, return(5)); forprime(p=2^n+1,, for(k=1,n, if(isprime(p+2^k) || isprime(p-2^k), next(2))); return(p)) \\ Charles R Greathouse IV, Jul 07 2017

Extensions

More terms from Michael De Vlieger, Jun 27 2017

a(15) corrected by Charles R Greathouse IV, Jul 07 2017