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On a Recursively Defined Sequence Involving the Prime Counting Function
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Altug Alkan

Graduate School of Science and Engineering

Piri Reis University

Istanbul

Turkey

Andrew R. Booker

School of Mathematics

University of Bristol

Woodland Road

Bristol, BS8 1UG

United Kingdom

Florian Luca

School of Mathematics

University of the Witwatersrand

Private Bag X3, Wits 2050

Johannesburg

South Africa

Research Group in Algebraic Structures and Applications

King Abdulaziz University

Jeddah

Saudi Arabia

Centro de Ciencias Matemáticas

UNAM

Morelia

Mexico

**Abstract:**

We prove some properties of sequence

A335294
from the

*On-Line Encyclopedia
of Integer Sequences*, defined by

*a*_{n} =
π(

*n*) - π (Σ

_{k=1}^{n−1}
*a*_{k}),
where π(

*x*) is the number of primes ≤

*x*.
In particular we show that
the sequence (

*a*_{n}) assumes every non-negative integral value infinitely
often.

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(Concerned with sequences
A335294
A335337.)

Received June 12 2020; revised version received January 27 2021.
Published in *Journal of Integer Sequences*,
January 31 2021.

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