login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062298 Number of nonprimes <= n. 48
1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 19, 20, 20, 21, 22, 23, 24, 25, 25, 26, 27, 28, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 42, 43, 43, 44, 45, 46, 47, 48, 48, 49, 50, 51, 51, 52, 52, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) = n - A000720(n). This is asymptotic to n - Li(n). Note that a(n) + A095117(n) = 2*n. - Jonathan Vos Post, Nov 22 2004

Same as number of primes between n and prime(n+1) and between n and prime(n)+1 (end points excluded); n prime -> a(n)=a(n-1), n composite-> a(n)=1+a(n-1). - David James Sycamore, Jul 23 2018

There exists at least one prime number between a(n) and n for n >= 3 (see the paper by Ya-Ping Lu attached in the links). - Ya-Ping Lu, Nov 27 2020

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

Ya-Ping Lu, Lower Bounds for the Number of Primes in Some Integer Intervals

FORMULA

a(n) = n - A000720(n).

a(n) = 1 + A065855(n). - David James Sycamore, Jul 23 2018

EXAMPLE

a(19) = 11 as there are 8 primes up to 19 (inclusive).

MAPLE

NumComposites := proc(N::posint) local count, i:count := 0:for i from 1 to N do if not isprime(i) then count := count + 1 fi:od: count; end:seq(NumComposites(binomial(k+1, k)), k=0..73); # Zerinvary Lajos, May 26 2008

A062298 := proc(n) n-numtheory[pi](n) ; end: seq(A062298(n), n=1..120) ; # R. J. Mathar, Sep 27 2009

MATHEMATICA

Table[n-PrimePi[n], {n, 80}] (* Harvey P. Dale, May 10 2012 *)

Accumulate[Table[If[PrimeQ[n], 0, 1], {n, 100}]] (* Harvey P. Dale, Feb 15 2017 *)

PROG

(PARI) a(n) = n-primepi(n); \\ Harry J. Smith, Aug 04 2009

(Haskell)

a062298 n = a062298_list !! (n-1)

a062298_list = scanl1 (+) $ map (1 -) a010051_list

-- Reinhard Zumkeller, Oct 10 2013

(MAGMA) [n - #PrimesUpTo(n): n in [1..100]]; // Vincenzo Librandi, Aug 05 2015

(Python)

from sympy import primepi

print([n - primepi(n) for n in range(1, 101)]) # Indranil Ghosh, Mar 29 2017

CROSSREFS

Cf. A000720, A101203, A010051, A065855.

Sequence in context: A321695 A197432 A255573 * A283371 A116579 A156253

Adjacent sequences:  A062295 A062296 A062297 * A062299 A062300 A062301

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jun 19 2001

EXTENSIONS

Corrected and extended by Vladeta Jovovic, Jun 22 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 12:16 EST 2021. Contains 349462 sequences. (Running on oeis4.)