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A105470 a(n)=1 if there is number of the form 6k+3 with prime(n) <= 6k+3 <= prime(n+1), otherwise 0. 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 (list; graph; refs; listen; history; text; internal format)
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: A189292 A331168 A331281 * A087429 A093075 A104120

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

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Last modified July 8 01:25 EDT 2020. Contains 335502 sequences. (Running on oeis4.)