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A090406
a(n) = PrimePi(n+3) - PrimePi(n).
3
2, 2, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1
OFFSET
1,1
COMMENTS
a(n) <= 2, with equality if and only if n=1 or n+1 is in A001359. - Robert Israel, Aug 14 2015
LINKS
Eric Weisstein's World of Mathematics, Hardy-Littlewood Conjectures
FORMULA
a(n) = A010051(n+1) + A010051(n+2) + A010051(n+3). - Robert Israel, Aug 14 2015
MAPLE
B:= [seq(numtheory:-pi(n), n=1..103)]:
B[4..-1] - B[1..-4]; # Robert Israel, Aug 14 2015
MATHEMATICA
Last[#]-First[#]&/@Partition[PrimePi[Range[110]], 4, 1] (* Harvey P. Dale, Feb 24 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Nov 29 2003
STATUS
approved