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

1,3

Comments

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

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A013603, A092131.

Sequence in context: A068219 A337461 A157031 * A088032 A348397 A066572

Adjacent sequences: A113210 A113211 A113212 * A113214 A113215 A113216

Keyword

nonn

Author

Zak Seidov, Jan 07 2006

Status

approved