A174695 Partial sums of A173950.

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, 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, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2

Offset: 1

Author

Giovanni Teofilatto, Nov 30 2010

Keywords

• sign

Comments

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

Links

• Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007352, A112632, A098044, A096630.

Concerning zeros or changes of sign, see also A096449 and A275939.

Programs

Maple

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:
A174695 := proc(n) add(A173950(i),i=1..n) ; end proc:
seq(A174695(n),n=1..90) ; # R. J. Mathar, Nov 30 2010

Mathematica

Accumulate[Table[Which[Divisible[Prime[n]+1,6],1,Divisible[Prime[n]-1,6],-1,True,0],{n,150}]] (* Harvey P. Dale, Apr 24 2019 *)

PARI

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

Formula

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