A128957 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 at least one of the primes 2,5 and is not divisible by at least one of the primes 3,7.

86, 857, 8571, 85715, 857142, 8571429, 85714286, 857142857, 8571428571, 85714285715, 857142857142, 8571428571429, 85714285714286, 857142857142857, 8571428571428571, 85714285714285715, 857142857142857142

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

Formula

a(n) = 10^n - floor(10^n/10) - floor(10^n/21) + floor(10^n/210).

Conjectures from Colin Barker, Nov 06 2017: (Start)

G.f.: x^2*(86 + 83*x + 84*x^2 + 89*x^3 + 81*x^4 + 90*x^5) / ((1 + x)*(1 - 10*x)*(1 - x + x^2)*(1 + x + x^2)).

a(n) = 9*a(n-1) + 9*a(n-2) + 9*a(n-3) + 9*a(n-4) + 9*a(n-5) + 10*a(n-6) for n>7.

(End)

Maple

f := n->10^n-floor(10^n/10)-floor(10^n/21)+floor(10^n/210);

Prog

(Magma) [10^n-Floor(10^n/10)-Floor(10^n/21)+Floor(10^n/210): n in [2..20]]; // Vincenzo Librandi, Oct 02 2011

Crossrefs

Cf. A092695.

Sequence in context: A272379 A262916 A262331 * A258584 A034277 A254702

Adjacent sequences: A128954 A128955 A128956 * A128958 A128959 A128960

Keyword

nonn

Author

Milan Janjic, Apr 28 2007

Status

approved