A128952 a(n) is equal to the number of positive integers m less than or equal to 10^n such that m is not divisible by the prime 3 and is not divisible by at least one of the primes 2, 5 and 7.

66, 657, 6572, 65715, 657143, 6571429, 65714286, 657142857, 6571428572, 65714285715, 657142857143, 6571428571429, 65714285714286, 657142857142857, 6571428571428572, 65714285714285715, 657142857142857143, 6571428571428571429, 65714285714285714286, 657142857142857142857

Offset

2,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (11,-11,11,-11,11,-10).

Formula

a(n) = 10^n - floor(10^n/3) - floor(10^n/70) + floor(10^n/210).

From Chai Wah Wu, May 09 2025: (Start)

a(n) = 11*a(n-1) - 11*a(n-2) + 11*a(n-3) - 11*a(n-4) + 11*a(n-5) - 10*a(n-6) for n > 7.

G.f.: x^2*(-70*x^5 + 69*x^4 - 76*x^3 + 71*x^2 - 69*x + 66)/((x - 1)*(10*x - 1)*(x^2 - x + 1)*(x^2 + x + 1)). (End)

Example

a(6) = 10^6 - floor(10^6/3) - floor(10^6/70) + floor(10^6/210) = 1000000 - floor(333333.333...) - floor(14285.714...) + floor(4761.904...) = 1000000 - 333333 - 14285 + 4761 = 657143. - Jon E. Schoenfield, Nov 18 2018

Maple

a := n->10^n-floor(10^n/3)-floor(10^n/70)+floor(10^n/210);

Mathematica

Table[With[{c=10^n}, c-Floor[c/3]-Floor[c/70]+Floor[c/210]], {n, 2, 20}] (* Harvey P. Dale, Jun 22 2022 *)

Prog

(Magma) [10^n-Floor(10^n/3)-Floor(10^n/70)+Floor(10^n/210): n in [2..20]]; // Vincenzo Librandi, Oct 02 2011
(PARI) a(n)=10^n-10^n\3-10^n\70+10^n\210 \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Cf. A092695.

Sequence in context: A233065 A129218 A046409 * A282050 A378741 A270258

Adjacent sequences: A128949 A128950 A128951 * A128953 A128954 A128955

Keyword

nonn,easy

Author

Milan Janjic, Apr 28 2007

Status

approved