A213902 - OEIS

%I #16 May 22 2021 04:30:31

%S 0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,0,1,0,0,1,0,1,2,0,0,0,0,0,4,0,1,0,2,

%T 0,1,1,0,1,1,0,2,0,0,0,3,3,0,0,0,1,0,2,1,1,1,0,1,0,0,2,4,0,0,0,4,1,2,

%U 0,0,1,2,1,1,0,1,2,0,2,2,0,2,0,1,0,1,2

%N Number of integers of the form 6*k+1 and 6*k-1 between prime(n) and prime(n+1).

%H Harvey P. Dale, <a href="/A213902/b213902.txt">Table of n, a(n) for n = 1..1000</a>

%t nn = 100; t = Join[{3}, Union[6*Range[nn] - 1, 6*Range[nn] + 1]]; cnt = 0; t2 = {}; Do[If[PrimeQ[t[[i]]], AppendTo[t2, cnt]; cnt = 0, cnt++], {i, Length[t]}]; t2 (* _T. D. Noe_, Jun 26 2012 *)

%t Module[{nn=90,k61},k61=Flatten[#+{1,5}&/@(6Range[0,Prime[nn+1]])];Table[ Count[ k61,_?(Prime[n]<#<Prime[n+1]&)],{n,nn}]] (* _Harvey P. Dale_, Mar 11 2019 *)

%o (Python)

%o # primes=[2,3,5,7,11,13,17,...]

%o for i in range(777):

%o     prime = primes[i]

%o     nextp = primes[i+1]

%o     k = nextp//6 - prime//6

%o     if k:

%o         k = (k-1)*2 + (prime%6==1) + (nextp%6==5)

%o     print(str(k), end=',')

%Y Cf. A001223.

%K nonn,easy

%O 1,24

%A _Alex Ratushnyak_, Jun 24 2012