A182067 a(n) = floor(n) - floor(n/2) - floor(n/3) - floor(n/5) + floor(n/30).

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

Offset

0

Comments

The sequence takes only the values 0 and 1 and is periodic with period 30. The sequence was used by Chebyshev to obtain the estimate for the prime counting function 0.92*x/log(x) <= #{primes <= x} <= 1.11*x/log(x), for x sufficiently large.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

H. G. Diamond, Elementary methods in the study of the distribution of prime numbers, Bull. Amer. Math. Soc., Vol.7 (3), 1982.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Mathematica

Table[Floor[n] - Floor[n/2] - Floor[n/3] - Floor[n/5] + Floor[n/30], {n, 0, 50}] (* G. C. Greubel, Aug 20 2017 *)

Prog

(PARI) a(n) = n - n\2 - n\3 - n\5 + n\30; \\ Michel Marcus, Jul 25 2017

Crossrefs

Cf. A211417.

Sequence in context: A286419 A257799 A089496 * A196147 A097325 A242647

Adjacent sequences: A182064 A182065 A182066 * A182068 A182069 A182070

Keyword

nonn,easy

Author

Peter Bala, Apr 11 2012

Status

approved