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

1,1

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]

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A327205 A219071 A072629 * A337802 A257531 A151763

Adjacent sequences: A164289 A164290 A164291 * A164293 A164294 A164295

Keyword

nonn

Author

Carlos Alves, Aug 12 2009

Status

approved