A082460 a(n) = pi(n) - a(n - 1) where pi(n) = A000720(n).

0, 1, 1, 1, 2, 1, 3, 1, 3, 1, 4, 1, 5, 1, 5, 1, 6, 1, 7, 1, 7, 1, 8, 1, 8, 1, 8, 1, 9, 1, 10, 1, 10, 1, 10, 1, 11, 1, 11, 1, 12, 1, 13, 1, 13, 1, 14, 1, 14, 1, 14, 1, 15, 1, 15, 1, 15, 1, 16, 1, 17, 1, 17, 1, 17, 1, 18, 1, 18, 1, 19, 1, 20, 1, 20, 1, 20, 1, 21, 1, 21, 1, 22, 1, 22, 1, 22, 1, 23, 1, 23, 1, 23, 1, 23, 1, 24, 1, 24, 1

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(1) = 0; after which, a(2n) = 1 and a(2n+1) = A000720(2n+1)-1. - Antti Karttunen, Nov 17 2019

a(n) = Sum_{k=1..n} (-1)^(n-k)*pi(k), where pi = A000720. - Ridouane Oudra, May 27 2023

Maple

with(numtheory): a:=proc(n) if n=1 then 0 elif (n mod 2)= 0 then 1 else pi(n)-1; fi: end proc: seq(a(n), n=1..100); # Ridouane Oudra, May 27 2023

Mathematica

f[x_] := PrimePi[x]-f[x-1] f[0]=0; Table[f[w], {w, 1, 128}]
nxt[{n_, a_}]:={n+1, PrimePi[n+1]-a}; NestList[nxt, {1, 0}, 100][[All, 2]] (* Harvey P. Dale, Jul 19 2021 *)

Prog

(PARI) k=pp=0; for(n=1, 99, pp+=isprime(n); k=pp-k; print1(k", ")) \\ Charles R Greathouse IV, May 15 2013
(PARI) A082460(n) = if(1==n, 0, if(!(n%2), 1, primepi(n)-1)); \\ Antti Karttunen, Nov 17 2019

Crossrefs

Cf. A000720.

Sequence in context: A327513 A327530 A084360 * A318573 A344774 A029227

Adjacent sequences: A082457 A082458 A082459 * A082461 A082462 A082463

Keyword

nonn

Author

Labos Elemer, Apr 26 2003

Extensions

Offset corrected to 1 and more terms from Antti Karttunen, Nov 17 2019

Status

approved