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A156660 Characteristic function of Sophie Germain primes. 17
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for characteristic functions

Wikipedia, Sophie Germain prime

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(a(k): 1<=k<=n). [From 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 Zmkeller_, May 01 2012

(PARI) a(n)=isprime(n)&&isprime(2*n+1) \\ Felix Fröhlich, Aug 11 2014

CROSSREFS

Cf. A156659.

Cf. A005384, A156874, A092816.

Sequence in context: A175337 A132380 A021913 * A155899 A117814 A062301

Adjacent sequences:  A156657 A156658 A156659 * A156661 A156662 A156663

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 13 2009

EXTENSIONS

Definition corrected by Daniel Forgues, Aug 04 2009

STATUS

approved

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Last modified January 17 09:45 EST 2018. Contains 297815 sequences.