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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

%I

%S 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,

%T 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,

%U 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

%N 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.

%C a(A002145(n)) = -1; a(A065090(n)) = 0; a(A002144(n)) = 1. [_Reinhard Zumkeller_, Oct 06 2011]

%H Reinhard Zumkeller, <a href="/A151763/b151763.txt">Table of n, a(n) for n = 1..10000</a>

%H N. Katz, <a href="http://dx.doi.org/10.1090/S0273-0979-09-01257-9">Lang-Trotter revisited</a>, Bull. Amer. Math. Soc., 46 (2009), 413-457.

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

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

%p seq(a(n),n=1..100); # _Robert Israel_, Aug 22 2014

%t 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 *)

%o (Haskell)

%o a151763 n | even n = 0

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

%o | otherwise = 0

%o -- _Reinhard Zumkeller_, Oct 06 2011

%Y Cf. A079260, A079261.

%Y Cf. A066520 (partial sums).

%K sign

%O 1,1

%A _N. J. A. Sloane_, Jun 22 2009

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Last modified August 5 08:46 EDT 2021. Contains 346464 sequences. (Running on oeis4.)