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A116127
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Number of numbers that are congruent to {2, 4} mod 6 between prime(n) and prime(n+1) inclusive.
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3
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1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 4, 2, 2, 0, 4, 0, 2, 2, 2, 2, 2, 0, 4, 0, 2, 0, 4, 4, 2, 0, 2, 2, 0, 4, 2, 2, 2, 0, 2, 2, 0, 4, 4, 2, 0, 2, 4, 2, 4, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 0, 4, 0, 2, 2, 2, 2, 2, 0, 2, 4, 2, 2, 2, 2, 2, 4, 0, 6, 2, 4, 2, 2, 0, 2
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OFFSET
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1,4
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COMMENTS
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For n > 2,
A001223(n) = 4 or 6 or 8 iff a(n) = 2,
A001223(n) = 10 or 12 or 14 iff a(n) = 4,
A001223(n) = 16 or 18 or 20 iff a(n) = 6,
and so on. This can be generalized to
A001223(n) = 3*k-2 or 3*k or 3*k+2 iff a(n) = k for k >= 2.
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LINKS
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MAPLE
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P:= select(isprime, [seq(i, i=5..1000, 2)]):
Delta:= P[2..-1]-P[1..-2]:
f:= t -> (t + 2*(t+1 mod 3) - 2)/3:
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PROG
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(Magma) [ #[ k: k in [NthPrime(n)..NthPrime(n+1)] | r eq 2 or r eq 4 where r is k mod 6 ]: n in [1..105] ]; /* Klaus Brockhaus, Apr 15 2007 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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