A113213 Smallest number m such that 2^n - m and 2^n + m are primes.

0, 1, 3, 3, 9, 3, 21, 15, 9, 15, 21, 3, 45, 135, 75, 15, 99, 93, 99, 315, 105, 105, 15, 75, 339, 117, 261, 183, 351, 453, 1281, 267, 675, 867, 819, 117, 69, 2343, 1995, 1005, 2949, 165, 741, 603, 315, 1287, 1629, 243, 519, 765, 165, 1233, 741, 1797, 339, 177

Offset: 1

Author

Zak Seidov, Jan 07 2006

Keywords

• nonn

Comments

For n>=3 all terms are multiples of 3.

Conjecture: a(n) = O(n^3). - Thomas Ordowski, Apr 20 2015

Examples

			a(1)=0 because 2^1 +/- 0 are primes; a(2)=1 because 2^2 -/+ 1 are primes;
a(33)=675 because 2^33 +/- 675 are closest (to each other) primes.
		

Links

• P. Poplin, Table of n, a(n) for n = 0..10000 (Terms after 8025 correspond to Fermat and Lucas PRP.)

Crossrefs

Cf. A013603, A092131.

Programs

Mathematica

f[n_]:=Module[{a=2^n,i=1},While[!PrimeQ[a+i]||!PrimeQ[a-i],i++];i]; Join[{0},Rest[Array[f,80]]]  (* Harvey P. Dale, Apr 25 2011 *)

PARI

a(n) = my(m=0); while(!(isprime(2^n+m) && isprime(2^n-m)), m++); m; \\ Michel Marcus, Apr 20 2015