A335716 a(n) = pi(pi(n)) - pi(Sum_{k=1..n-1} a(k)) with a(1) = 0.

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

Offset

1

Comments

Conjecture: a(n) hits every nonnegative integer.

Links

Altug Alkan, Table of n, a(n) for n = 1..10000

Altug Alkan, Andrew R. Booker, and Florian Luca, On a recursively defined sequence involving the prime counting function, arXiv:2006.08013 [math.NT], 2020.

Example

a(10861) = pi(pi(10861)) - pi(Sum_{k=1..10860} a(k)) = 216 - 214 = 2.

Mathematica

a[1] = s[1] = 0; a[n_] := a[n] = PrimePi@ PrimePi@ n - PrimePi@ s[n-1]; s[n_] := s[n] = s[n-1] + a[n]; Array[a, 100] (* Giovanni Resta, Jun 19 2020 *)

Prog

(PARI) a=vector(10^2); a[1] = 0; for(n=2, #a, a[n] = primepi(primepi(n)) - primepi(sum(k=1, n-1, a[k]))); a

Crossrefs

Cf. A000720, A335294.

Sequence in context: A354874 A014306 A374220 * A138150 A271591 A287790

Adjacent sequences: A335713 A335714 A335715 * A335717 A335718 A335719

Keyword

nonn,changed

Author

Altug Alkan, Jun 18 2020

Status

approved