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A273514
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a(n) is the number of arithmetic progressions m < n < p (three numbers in arithmetic progression) such that m and p contain no 2's in their ternary representation.
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4
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0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 8, 8, 8, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2
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OFFSET
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0,3
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COMMENTS
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This is a recursive sequence that gives the number of times n is rejected from A005836, if n is the middle member of an arithmetic triple whose first and last terms are contained in A005836.
Also, a(n) is the number of unordered pairs of members of A005836 whose average (arithmetic mean) is n.
Local maxima occur at a(A125857(n)).
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LINKS
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FORMULA
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a(0) = 0, a(n) = a(3n) = a(3n+1); if a(n) = 0, a(9n + 2) = 2, otherwise a(9n + 2) = 4a(n); a(9n + 5) = a(9n + 6) = a(9n + 7) = a(9n + 8) = a(3n + 2).
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EXAMPLE
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a(2) = 2 because there are two arithmetic triples a < 2 < b such that a and b are members of A005836: 0, 2, 4 and 1, 2, 3.
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PROG
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(PARI) precCantor(n)=my(v=digits(n, 3)); for(i=1, #v, if(v[i]==2, for(j=i, #v, v[j]=1); break)); fromdigits(v, 2)
a(n)=if(n==0, return(0)); sum(i=0, precCantor(n-1), my(m=fromdigits(digits(i, 2), 3)); vecmax(digits(2*n-m, 3))<2) \\ Charles R Greathouse IV, Jun 17 2016
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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