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

0,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A120937.

Sequence in context: A338977 A090686 A082277 * A155851 A019267 A053664

Adjacent sequences: A289151 A289152 A289153 * A289155 A289156 A289157

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 26 2017

Extensions

More terms from Michael De Vlieger, Jun 27 2017

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

Status

approved