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A151763 If n is a prime == 1 mod 4 then a(n) = 1, if n is a prime == 3 mod 4 then a(n) = -1, otherwise a(n) = 0. 10
0, 0, -1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(A002145(n)) = -1; a(A065090(n)) = 0; a(A002144(n)) = 1. [Reinhard Zumkeller, Oct 06 2011]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

N. Katz, Lang-Trotter revisited, Bull. Amer. Math. Soc., 46 (2009), 413-457.

FORMULA

a(n) = (2 - n mod 4) * A010051(n).

MAPLE

a:= proc(n) if n::odd and isprime(n) then 2 - (n mod 4) else 0 fi end proc:

seq(a(n), n=1..100); # Robert Israel, Aug 22 2014

MATHEMATICA

a[n_] := Which[!PrimeQ[n], 0, m = Mod[n, 4]; m == 1, 1, m == 3, -1, True, 0]; Array[a, 105] (* Jean-Fran├žois Alcover, Dec 03 2016 *)

PROG

(Haskell)

a151763 n | even n         = 0

          | a010051 n == 1 = 2 - n `mod` 4

          | otherwise      = 0

-- Reinhard Zumkeller, Oct 06 2011

CROSSREFS

Cf. A079260, A079261.

Cf. A066520 (partial sums).

Sequence in context: A060510 A072629 A164292 * A022925 A144607 A051840

Adjacent sequences:  A151760 A151761 A151762 * A151764 A151765 A151766

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Jun 22 2009

STATUS

approved

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Last modified December 11 02:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)