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a(n) = 1 iff n-th prime has an odd digit sum.
+10
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0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1
COMMENTS
Characteristic function of A200260.
MATHEMATICA
If[OddQ[Total[IntegerDigits[#]]], 1, 0]&/@Prime[Range[100]] (* Harvey P. Dale, Jul 08 2019 *)
PROG
(Magma) [IsOdd(&+Intseq(NthPrime(n))) select 1 else 0: n in [1..100]]; // Bruno Berselli, Nov 15 2011
a(n) = number of primes with an even digit sum among the first n primes minus the number with an odd digit sum.
+10
1
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
FORMULA
a(n)=sum_{k=1...n} (-1)^ A007605(n).
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(PARI) s=0; vector(90, n, s+=(-1)^ A007953(prime(n)))
CROSSREFS
Cf. A007605, A007953, A130911, A200259, A200260, A119449, A119450, A200261, A200262, A200263, A200264.
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