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A156660 Characteristic function of Sophie Germain primes.

%I A156660 #36 Nov 06 2022 07:47:59
%S A156660 0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
%T A156660 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A156660 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A156660 Characteristic function of Sophie Germain primes.
%H A156660 Reinhard Zumkeller, <a href="/A156660/b156660.txt">Table of n, a(n) for n = 0..10000</a>
%H A156660 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sophie_Germain_prime">Sophie Germain prime</a>
%H A156660 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A156660 a(n) = if n and also 2*n+1 is prime then 1 else 0.
%F A156660 a(A005384(n)) = 1; a(A138887(n)) = 0; a(A053176(n)) = 0.
%F A156660 A156874(n) = Sum_{k=1..n} a(k). - _Reinhard Zumkeller_, Feb 18 2009
%F A156660 a(n) = A010051(n)*A010051(2*n+1).
%F A156660 For n>1 a(n) = floor((floor(phi(n)/(n-1)) + floor(phi(2*n+1)/(2*n)))/2). - _Enrique Pérez Herrero_, Apr 28 2012
%F A156660 For n>1 a(n) = floor(phi(2*n^2+n)/(2*n^2-2*n)). - _Enrique Pérez Herrero_, May 02 2012
%o A156660 (Haskell)
%o A156660 a156660 n = fromEnum $ a010051 n == 1 && a010051 (2 * n + 1) == 1
%o A156660 -- _Reinhard Zumkeller_, May 01 2012
%o A156660 (PARI) a(n)=isprime(n)&&isprime(2*n+1) \\ _Felix Fröhlich_, Aug 11 2014
%Y A156660 Cf. A156659.
%Y A156660 Cf. A005384, A156874, A092816.
%K A156660 nonn
%O A156660 0,1
%A A156660 _Reinhard Zumkeller_, Feb 13 2009
%E A156660 Definition corrected by _Daniel Forgues_, Aug 04 2009