Search: id:A070750
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%I A070750
%S A070750 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A070750 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A070750 1,1
%V A070750 0,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,
               1,1,-1,-1,1,
%W A070750 -1,1,-1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,-1,1,1,-1,
               1,-1,-1,1,1,
%X A070750 -1,1,-1,1,1,-1
%N A070750 sin(prime(n)*pi/2), where prime=A000040, pi=3.1415...
%C A070750 Also imaginary part of primes mapped as defined in A076340, A076341: 
               a(n)=A076341(A000040(n)), real part = A076342.
%C A070750 Legendre symbol (-1/prime(n)) for n > 1. - T. D. Noe (noe(AT)sspectra.com), 
               Nov 05 2003
%H A070750 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LegendreSymbol.html">Legendre Symbol</a>
%F A070750 a(n) = 2 - prime(n) mod 4.
%F A070750 a(n) = (-1)^((prime(n)-1)/2) for n > 1 - T. D. Noe (noe(AT)sspectra.com), 
               Nov 05 2003
%e A070750 p=4*k+1 (see A002144): a(p) = sin((4*k+1)*pi/2) = sin(2*k*pi+pi/2) = 
               sin(pi/2) = 1; p=4*k+3 (see A002145): a(p) = sin((4*k+3)*pi/2) = 
               sin(2*k*pi+3*pi/2) = sin(3*pi/2) = -1.
%Y A070750 Cf. A070748, A070749, A002144, A002145.
%Y A070750 Sequence in context: A011596 A011597 A070747 this_sequence A011598 A011599 
               A011600
%Y A070750 Adjacent sequences: A070747 A070748 A070749 this_sequence A070751 A070752 
               A070753
%K A070750 sign,nice
%O A070750 1,1
%A A070750 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 04 2002

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