A272576 - OEIS

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

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OFFSET

0,3

COMMENTS

Also, numbers not ending with the digit 8 or 9, i.e., with final digit at most 7.

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

Zhuorui He, Table of n, a(n) for n = 0..10000

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

Index entries for 10-automatic sequences.

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

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 *)

PROG

(Magma) k:=10; f:=func<k, m | Floor(m*k/(k-1))>; [f(k, f(k-1, n)): n in [0..70]];

(SageMath)

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

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

CROSSREFS

Cf. similar sequences listed in A272574.

Cf. A008592 (final digit at most 0), A197652 (at most 1), A391163 (at most 2), A390774 (at most 3), A293292 (at most 4), A391164 (at most 5), A001477 (at most 9).

Cf. A007094, A039155.

Sequence in context: A336064 A039269 A039207 * A039155 A007094 A000433

Adjacent sequences: A272573 A272574 A272575 * A272577 A272578 A272579

KEYWORD

nonn,easy,base

AUTHOR

Bruno Berselli, May 03 2016

STATUS

approved