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A331112 Sum of the digits of the n-th prime number in balanced ternary.

%I A331112 #15 Jan 13 2020 17:45:52
%S A331112 0,1,-1,1,1,3,-1,1,-1,1,3,3,-3,-1,-1,-1,-1,1,3,-1,1,1,1,1,1,1,3,1,3,1,
%T A331112 -1,-3,-1,1,-3,-1,1,1,-1,1,-1,1,1,3,1,3,1,1,1,3,-1,-1,1,1,-1,1,1,3,3,
%U A331112 3,5,-1,3,-1,1,1,3,5,1,3,3,3,-3,-1,-1,-3,-1,-1,-3,1,-3,-1,-1,1,1,1,-3,-1,-1,1,-1,-1,1,-1,3,-1,-1,1,3,1
%N A331112 Sum of the digits of the n-th prime number in balanced ternary.
%H A331112 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%F A331112 a(n) = A065363(A000040(n)). - _Alois P. Heinz_, Jan 09 2020
%e A331112 Using T for -1 and _bt as suffix for balanced ternary: 2_10 = 1T_bt, sum of digits is zero; 3_10 = 10_bt, sum of digits is 1 and 5_10 = 1TT, sum of digits = -1.
%p A331112 b:= proc(n) `if`(n=0, 0, (d-> `if`(d=2,
%p A331112       b(q+1)-1, d+b(q)))(irem(n, 3, 'q')))
%p A331112     end:
%p A331112 a:= n-> b(ithprime(n)):
%p A331112 seq(a(n), n=1..100);  # _Alois P. Heinz_, Jan 09 2020
%o A331112 (C)
%o A331112 #include <stdio.h>
%o A331112 #include <math.h>
%o A331112 #define N 1000 /* Largest prime considered - 1  */
%o A331112 char x[N];
%o A331112 int main()
%o A331112 {
%o A331112   int i, n, v, s, r;
%o A331112   for (i=4; i<N; i+=2)
%o A331112     x[i] = 1;
%o A331112   for (n=3; n<sqrt(N*1.0); n +=2)
%o A331112     for (i=n+n; i<N; i+=n)
%o A331112       x[i] = 1;
%o A331112   for (n = 2; n < N; n++) {
%o A331112     if (x[n] == 0) {
%o A331112       v = n;
%o A331112       s = 0;
%o A331112       while (v != 0) {
%o A331112         r = v % 3;
%o A331112         if (r == 2)
%o A331112           r = -1;
%o A331112         s = s + r;
%o A331112         v = (v - r) / 3;
%o A331112       }
%o A331112       printf("%d,",s);
%o A331112     }
%o A331112   }
%o A331112   printf("\n");
%o A331112 }
%Y A331112 See A007605 (sum of digits of primes in base 10); A239619 (sum of digits of primes in base 3).
%Y A331112 Cf. A000040, A065363, A117966.
%K A331112 sign,base,easy
%O A331112 1,6
%A A331112 _Thomas König_, Jan 09 2020