A212361 Number of primes between two consecutive prime triples (p, p+2, p+6).

0, 0, 3, 10, 0, 12, 3, 12, 2, 17, 24, 23, 3, 1, 27, 21, 3, 10, 6, 0, 14, 30, 13, 8, 16, 1, 45, 3, 65, 23, 5, 17, 27, 6, 13, 43, 9, 15, 12, 3, 28, 25, 0, 14, 59, 70, 114, 18, 13, 5, 21, 37, 60, 1, 93, 5, 1, 71, 54, 36, 86, 7, 67, 6, 9, 0, 15, 16, 30, 108, 7, 31

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(4)= 10 because between the 4th and 5th prime triples there are 10 primes: (41,43,47) 53, 59 61, 67, 71, 73, 79, 83, 89, 97 (101,103,107).

Maple

with(numtheory):T:=array(1..1000):k:=1:for n from 1 to 4000 do:p:=ithprime(n):if type(p+2, prime)=true and type(p+6, prime) = true then T[k]:=p:T[k+1]:=p+6:k:=k+2:else fi:od:for m from 2 by 2 to k-2 do: p1:= T[m]:p2:=T[m+1]:i:=0:for q from p1+1 to p2-1 do:if type(q, prime)=true then i:=i+1:else fi:od: printf(`%d, `, i):od:

Mathematica

If[#>0, #-1, #]&/@(PrimePi[#[[1]]]-PrimePi[#[[2]]]&/@({#[[2, 1]], #[[1, 3]]}&/@ Partition[Select[Partition[Prime[Range[2000]], 3, 1], Differences[#]=={2, 4}&], 2, 1])) (* Harvey P. Dale, Jun 08 2016 *)

Crossrefs

Cf. A048614, A022004.

Sequence in context: A137044 A188545 A336747 * A011998 A278759 A280752

Adjacent sequences: A212358 A212359 A212360 * A212362 A212363 A212364

Keyword

nonn

Author

Michel Lagneau, Jun 29 2012

Status

approved