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A156660
Characteristic function of Sophie Germain primes.
21
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, 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, 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
OFFSET
0,1
FORMULA
a(n) = if n and also 2*n+1 is prime then 1 else 0.
a(A005384(n)) = 1; a(A138887(n)) = 0; a(A053176(n)) = 0.
A156874(n) = Sum_{k=1..n} a(k). - Reinhard Zumkeller, Feb 18 2009
a(n) = A010051(n)*A010051(2*n+1).
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
For n>1 a(n) = floor(phi(2*n^2+n)/(2*n^2-2*n)). - Enrique Pérez Herrero, May 02 2012
PROG
(Haskell)
a156660 n = fromEnum $ a010051 n == 1 && a010051 (2 * n + 1) == 1
-- Reinhard Zumkeller, May 01 2012
(PARI) a(n)=isprime(n)&&isprime(2*n+1) \\ Felix Fröhlich, Aug 11 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 13 2009
EXTENSIONS
Definition corrected by Daniel Forgues, Aug 04 2009
STATUS
approved