A046929 Width of moat of composite numbers surrounding n-th prime.

0, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 5, 1, 1, 3, 1, 1, 3, 3, 5, 3, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 5, 3, 3, 5, 1, 1, 1, 1, 1, 1, 11, 3, 1, 1, 3, 1, 1, 5, 5, 5, 1, 1, 3, 1, 1, 9, 3, 1, 1, 3, 5, 5, 1, 1, 3, 5, 5, 5, 3, 3, 5, 3, 3, 7, 1, 1, 1, 1, 3, 3, 5, 3, 1, 1, 3, 7, 3, 3

Offset

1,9

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Jean-François Alcover, Frequency distribution up to 10^6 terms.

Example

23 has a buffer of 3 composites around it on each side: 20,21,22,23,24,25,26.

Maple

with(numtheory); a := i->min(ithprime(n)-ithprime(n-1)-1, ithprime(n+1)-ithprime(n)-1);

Mathematica

a[n_] := Min[Prime[n] - Prime[n-1] - 1, Prime[n+1] - Prime[n] - 1]; a[1] = 0; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Apr 16 2013 *)
Join[{0}, Min[Differences[#]]&/@Partition[Prime[Range[100]], 3, 1]-1] (* Harvey P. Dale, Feb 24 2014 *)

Crossrefs

Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.

Sequence in context: A060266 A073310 A174414 * A377776 A068695 A110787

Adjacent sequences: A046926 A046927 A046928 * A046930 A046931 A046932

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved