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A212361 Number of primes between two consecutive prime triples (p, p+2, p+6). 1

%I

%S 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,

%T 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,

%U 60,1,93,5,1,71,54,36,86,7,67,6,9,0,15,16,30,108,7,31

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

%H Harvey P. Dale, <a href="/A212361/b212361.txt">Table of n, a(n) for n = 1..1000</a>

%e 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).

%p 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:

%t 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 *)

%Y Cf. A048614, A022004.

%K nonn

%O 1,3

%A _Michel Lagneau_, Jun 29 2012

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Last modified September 28 04:28 EDT 2022. Contains 357063 sequences. (Running on oeis4.)