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A174695
Partial sums of A173950.
2
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
1,10
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
FORMULA
a(n) = A112632(n)-1. - M. F. Hasler, Oct 09 2011
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 *)
PROG
(PARI) s=0; forprime(p=1, 999, print1(s+=if(p%3-1, p>3, -1)", ")) \\ M. F. Hasler, Oct 09 2011
CROSSREFS
Concerning zeros or changes of sign, see also A096449 and A275939.
Sequence in context: A346700 A301574 A272728 * A337622 A165577 A259776
KEYWORD
sign
AUTHOR
Giovanni Teofilatto, Nov 30 2010
STATUS
approved