A105470 a(n)=1 if there is number of the form 6k+3 with prime(n) <= 6k+3 <= prime(n+1), otherwise 0.

1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1

Offset

1,1

Comments

Except for the first pair of primes and for twin primes there is always at least one number of the form 6n+3 between two successive primes.

Links

Table of n, a(n) for n=1..105.

Example

a(3)=0 because between prime(3) and prime(4) there are no numbers of the form 6k+3;
a(4)=1 because between prime(4) and prime(5) there is one number of the form 6k+3: 9.

Mathematica

f[n_] := Count[Table[Mod[k, 6], {k, Prime[n], Prime[n + 1]}], 3]; Table[If[f[n] == 0, 0, 1], {n, 120}] (* Ray Chandler, Oct 17 2006 *)
Join[{1, 1}, If[Last[#]-First[#]==2, 0, 1]&/@Partition[Prime[Range[ 3, 200]], 2, 1]] (* Harvey P. Dale, Nov 27 2013 *)

Crossrefs

Cf. A100810, A106002.

Sequence in context: A331168 A331281 A347950 * A359824 A087429 A093075

Adjacent sequences: A105467 A105468 A105469 * A105471 A105472 A105473

Keyword

easy,nonn

Author

Giovanni Teofilatto, May 02 2005

Extensions

Edited by Ray Chandler, Oct 17 2006

Status

approved