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A199339
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a(n) = number of primes with an even digit sum among the first n primes minus the number with an odd digit sum.
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1
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1, 0, -1, -2, -1, 0, 1, 2, 1, 0, 1, 2, 1, 0, -1, 0, 1, 0, -1, 0, 1, 2, 1, 0, 1, 2, 3, 4, 5, 4, 5, 4, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 1, 0, -1, -2, -1, -2, -3, -4, -3, -2, -3, -2, -1, -2, -3, -2, -1, -2, -3, -2, -1, -2, -3, -4, -5, -6, -5, -4, -5, -6, -5, -6
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n)=sum_{k=1...n} (-1)^A007605(n).
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EXAMPLE
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a(1)=1 because the first prime has an even sum of digits.
a(2)=0, a(3)=-1, a(4)=-2 because the following primes (3,5,7) have odd sum of digits.
a(5)=-1, a(6)=0, a(7)=1, a(8)=2 because the 5th, 6th, 7th and 8th prime (11, 13, 17, 19) have an even sum of digits.
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MATHEMATICA
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a[1] := 1; a[n_] := a[n] = a[n - 1] + (-1)^(Plus@@IntegerDigits[Prime[n]]); Table[a[n], {n, 74}] (* Alonso del Arte, Nov 14 2011 *)
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PROG
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(PARI) s=0; vector(90, n, s+=(-1)^A007953(prime(n)))
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CROSSREFS
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Cf. A007605, A007953, A130911, A200259, A200260, A119449, A119450, A200261, A200262, A200263, A200264.
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KEYWORD
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sign,base
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AUTHOR
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STATUS
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approved
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