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A174695 Partial sums of A173950. 1


%S 0,0,1,0,1,0,1,0,1,2,1,0,1,0,1,2,3,2,1,2,1,0,1,2,1,2,1,2,1,2,1,2,3,2,

%T 3,2,1,0,1,2,3,2,3,2,3,2,1,0,1,0,1,2,1,2,3,4,5,4,3,4,3,4,3,4,3,4,3,2,

%U 3,2,3,4,3,2,1,2,3,2

%N Partial sums of A173950.

%C Since this sequence equals A112632(n)-1, and A007352 gives the primes at which the sign of A112632 changes, we have a change of sign in the present sequence not exactly at the primes listed in A007352, but earlier for changes to negative sign, and later for the opposite changes. Moreover, a change of sign in either of the sequences corresponds not necessarily to a change of sign (in the strict sense, i.e., regarding 0 as a number with the same sign as the preceding term) in the other one. - M. F. Hasler, Oct 09 2011

%H Franklin T. Adams-Watters, <a href="/A174695/b174695.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A112632(n)-1. - M. F. Hasler, Oct 09 2011

%p A173950 := proc(n) if (ithprime(n)+1) mod 6 = 0 then 1; elif (ithprime(n)-1) mod 6 = 0 then -1; else 0 ; end if; end proc:

%p A174695 := proc(n) add(A173950(i),i=1..n) ; end proc:

%p seq(A174695(n),n=1..90) ; # R. J. Mathar, Nov 30 2010

%o (PARI) s=0;forprime(p=1,999,print1(s+=if(p%3-1,p>3,-1)",")) \\ - M. F. Hasler, Oct 09 2011

%Y Cf. A007352, A112632, A098044, A096630.

%K sign

%O 1,10

%A _Giovanni Teofilatto_, Nov 30 2010

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.