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A007095 Numbers in base 9.
(Formerly M0490)
51
0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also numbers without 9 as a digit.

Complement of A011539: A102683(a(n)) = 0; A068505(a(n)) != a(n)). - Reinhard Zumkeller, Dec 29 2011

The sum of the inverses of these numbers from a(1)=1 to infinity, called the Kempner series, is convergent towards a limit: 22.92067... whose decimal expansion is in A082838. - Bernard Schott, Dec 29 2018

REFERENCES

Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992

Index entries for 10-automatic sequences.

FORMULA

a(0)=0 a(n)=10*a(n/9) if n==0 (mod 9) a(n)=a(n-1)+1 otherwise. - Benoit Cloitre, Dec 22 2002

MAPLE

A007095 := proc(n) local l: if(n=0)then return 0: fi: l:=convert(n, base, 9): return op(convert(l, base, 10, 10^nops(l))): end: seq(A007095(n), n=0..67); # Nathaniel Johnston, May 06 2011

MATHEMATICA

Table[ FromDigits[ IntegerDigits[n, 9]], {n, 0, 75}]

PROG

(PARI) a(n)=if(n<1, 0, if(n%9, a(n-1)+1, 10*a(n/9)))

(PARI) a(n) = fromdigits(digits(n, 9)); \\ Michel Marcus, Dec 29 2018

(MAGMA) [ n: n in [0..74] | not 9 in Intseq(n) ];  // Bruno Berselli, May 28 2011

(sh) seq 0 1000 | grep -v 9; # Joerg Arndt, May 29 2011

(Haskell)

a007095 = f . subtract 1 where

   f 0 = 0

   f v = 10 * f w + r   where (w, r) = divMod v 9

-- Reinhard Zumkeller, Oct 07 2014, Dec 29 2011

CROSSREFS

Cf. A000042, A004184, A004728, A007088, A007089, A007090, A007091, A007092, A007093, A007094, A037479.

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8).

Cf. A031076, A031087.

CF. A082838.

Sequence in context: A316495 A036741 A037479 * A088481 A194151 A020663

Adjacent sequences:  A007092 A007093 A007094 * A007096 A007097 A007098

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

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Last modified January 24 03:59 EST 2019. Contains 319412 sequences. (Running on oeis4.)