On a Recursively Defined Sequence Involving the Prime Counting Function

Altug Alkan; Andrew R Booker; Florian Luca

On a Recursively Defined Sequence Involving the Prime Counting Function

Altug Alkan
, Andrew R Booker
, Florian Luca

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We prove some properties of sequence A335294 from the On-Line Encyclopedia of
Integer Sequences, defined by an = π(n) − π Pn−1 k=1 ak, where π(x) is the number of primes ≤ x. In particular we show that the sequence (an)
assumes every non-negative integral value infinitely often.

Original language	English
Article number	21.3.1
Number of pages	18
Journal	Journal of Integer Sequences
Volume	24
Publication status	Published - 31 Jan 2021

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title = "On a Recursively Defined Sequence Involving the Prime Counting Function",

abstract = "We prove some properties of sequence A335294 from the On-Line Encyclopedia of Integer Sequences, defined by an = π(n) − π Pn−1 k=1 ak, where π(x) is the number of primes ≤ x. In particular we show that the sequence (an) assumes every non-negative integral value infinitely often.",

author = "Altug Alkan and Booker, \{Andrew R\} and Florian Luca",

year = "2021",

month = jan,

day = "31",

language = "English",

volume = "24",

journal = "Journal of Integer Sequences",

issn = "1530-7638",

publisher = "University of Waterloo",

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TY - JOUR

T1 - On a Recursively Defined Sequence Involving the Prime Counting Function

AU - Alkan, Altug

AU - Booker, Andrew R

AU - Luca, Florian

PY - 2021/1/31

Y1 - 2021/1/31

N2 - We prove some properties of sequence A335294 from the On-Line Encyclopedia of Integer Sequences, defined by an = π(n) − π Pn−1 k=1 ak, where π(x) is the number of primes ≤ x. In particular we show that the sequence (an) assumes every non-negative integral value infinitely often.

AB - We prove some properties of sequence A335294 from the On-Line Encyclopedia of Integer Sequences, defined by an = π(n) − π Pn−1 k=1 ak, where π(x) is the number of primes ≤ x. In particular we show that the sequence (an) assumes every non-negative integral value infinitely often.

M3 - Article (Academic Journal)

SN - 1530-7638

VL - 24

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

M1 - 21.3.1

ER -

On a Recursively Defined Sequence Involving the Prime Counting Function

Abstract

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