A272576 a(n) = f(10, f(9, n)), where f(k,m) = floor(m*k/(k-1)).

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 90

Offset: 0

Author

Bruno Berselli, May 03 2016

Keywords

• nonn
• easy
• base

Comments

Also, numbers not ending with the digit 8 or 9.

The initial terms coincide with those of A007094 and A039155. First disagreement is after 77 (index 63): a(64) = 80, A007094(64) = 100 and A039155(65) = 89.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).
• Index entries for 10-automatic sequences.

Crossrefs

Cf. similar sequences listed in A272574.

Programs

Magma

k:=10; f:=func; [f(k,f(k-1,n)): n in [0..70]];

Maple

f := (k, m) -> floor(m*k/(k-1)):
a := n -> f(10, f(9,n)):
seq(a(n), n = 0..72); # Peter Luschny, May 03 2016

Mathematica

f[k_, m_] := Floor[m*k/(k-1)];
a[n_] := f[10, f[9, n]];
Table[a[n], {n, 0, 72}] (* Jean-François Alcover, May 09 2016 *)
LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,7,10},90] (* Harvey P. Dale, Jun 22 2017 *)

PARI

is(n)=n%10<8 \\ Charles R Greathouse IV, Feb 13 2017

Sage

f = lambda k, m: floor(m*k/(k-1))
a = lambda n: f(10, f(9, n))
[a(n) for n in range(73)] # Peter Luschny, May 03 2016

Formula

G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + 3*x^7)/((1 + x)*(1 - x)^2*(1 + x^2) *(1 + x^4)).

a(n) = a(n-1) + a(n-8) - a(n-9).

a(n) = 1.25n + O(1). - Charles R Greathouse IV, Nov 07 2022