A164292 Binary sequence identifying the twin primes (characteristic function of twin primes: 1 if n is a twin prime else 0).

0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 1, 0, 0

Offset: 1

Author

Carlos Alves, Aug 12 2009

Keywords

• nonn

Comments

Similar to prime binary digit sequence A010051.

In decimal notation A164292=0.1646823906345389353962381...

See also A164293 (similar to prime decimal sequence A051006).

a(A001097(n))=1; a(A001359(n))=1; a(A006512(n))=1. - Reinhard Zumkeller, Mar 29 2010

Characteristic function of A001097. - Georg Fischer, Aug 04 2021

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for characteristic functions [From _Reinhard Zumkeller_, Mar 29 2010]

Crossrefs

Cf. A001097, A010051, A051006, A057427, A129950, A164293.

Programs

Haskell

a164292 1 = 0
a164292 2 = 0
a164292 n = signum (a010051' n * (a010051' (n - 2) + a010051' (n + 2)))
-- Reinhard Zumkeller, Feb 03 2014

Mathematica

Table[(PrimePi[n] - PrimePi[n - 1]) * Ceiling[(PrimePi[n + 2] - PrimePi[n + 1] + PrimePi[n - 2] - PrimePi[n - 3])/2], {n, 100}] (* Wesley Ivan Hurt, Jan 31 2014 *)
Table[If[PrimeQ[n]&&AnyTrue[n+{2,-2},PrimeQ],1,0],{n,120}] (* Harvey P. Dale, Jan 04 2025 *)

Formula

a(n) = A057427(A010051(n)*(A010051(n-2)+A010051(n+2))), for n>2. - Reinhard Zumkeller, Mar 29 2010

a(n) = c(n) * ceiling(( c(n+2) + c(n-2) )/2), where c is the prime characteristic. - Wesley Ivan Hurt, Jan 31 2014