A131377 a(n) = (pi(n)+1) mod 2.

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

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 04 2007

Keywords

• easy
• nonn

Comments

Old name was: Starting with 1, the sequence a(n) changes from 1 to 0 or back when the next number n is a prime.

Möbius transform of A345220(n). - Wesley Ivan Hurt, Jul 05 2025

Examples

			n = 0, 1, 2, 3, 4, 5, etc..
a(n)= 1, 1, 0, 1, 1, 0, etc.
Starting with 1 the sequence changes when we move from 1 to 2 because 2 is prime, again from 2 to 3 because also 3 is prime, then from 4 to 5 being 5 prime and so on.
		

Crossrefs

Cf. A000035 (n mod 2), A000720 (pi), A008683 (mu), A036234, A131378, A345220.

Cf. A071986. - Omar E. Pol, Feb 19 2011

Programs

Maple

P:=proc(n) local i,k; k:=1; for i from 0 by 1 to n do if isprime(i) then if k=1 then k:=0; else k:=1; fi; fi; print(k); od; end: P(100);

Mathematica

Table[Mod[PrimePi[n] + 1, 2], {n, 0, 100}] (* Wesley Ivan Hurt, Jul 05 2025 *)

Formula

a(n) = 1 - A071986(n).

From Wesley Ivan Hurt, Jul 05 2025: (Start)

a(n) = A000035(A036234(n)).

a(n) = Sum_{d|n} A345220(d) * mu(n/d). (End)

Extensions

New name from Wesley Ivan Hurt, Jul 05 2025