A059959 Distance of 2^n from its nearest prime neighbor and in case of a tie, choose the smaller.

-1, 0, 1, 1, -1, 1, 3, 1, -1, 3, 3, -5, 3, 1, 3, -3, -1, 1, -3, 1, 3, 9, 3, -9, 3, -35, 5, -29, -3, 3, -3, 1, 5, 9, -25, 31, 5, -9, -7, 7, -15, 21, 11, -29, -7, 55, -15, -5, -21, -69, 27, -21, -21, -5, 33, -3, 5, -9, 27, 55, -33, 1, 57, 25, -13, 49, 5, -3, 23, 19, -25, -11, -15, -29, 35, -33, 15, -11, -7, -23, -13, -17, -9, 55, -3, 19

Offset: 0

Author

Labos Elemer, Mar 02 2001

Keywords

• sign

Examples

			n=19, 2^19=524288, prevprime(524288)=524287, nextprime(524288)=524309, so min{21,1}=1=a(19).
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..10000 (terms 0-4500 from Giovanni Resta)

Crossrefs

Cf. A000079, A117387, A013597, A013603, A014210, A014234, A058249.

Programs

Maple

with(numtheory): [seq(min(nextprime(2^i)-2^i, 2^i-prevprime(2^i)), i=2..100)];

Mathematica

f[n_] := Block[{k = 0}, While[ !PrimeQ[2^n -k] && !PrimeQ[2^n +k], k++]; If[ PrimeQ[2^n -k], k, -k]]; Array[f, 70, 0] (* Robert G. Wilson v, Mar 14 2006 and modified Jan 12 2024 *)

Formula

a(n) = A000079(n) - A117387(n).

Extensions

Signs added by Robert G. Wilson v, Mar 14 2006