

A052405


Numbers without 3 as a digit.


16



0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89
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OFFSET

1,3


COMMENTS

This sequence also represents the minimal number of straight lines of a covering tree to cover n X n points arranged in a symmetrical grid.  Marco Ripà, Sep 20 2018


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
Index entries for 10automatic sequences.


FORMULA

a(n) >> n^k with k = log(10)/log(9) = 1.0479....  Charles R Greathouse IV, Oct 16 2012
a(n) = replace digits d > 2 by d + 1 in base9 representation of n  1.  Reinhard Zumkeller, Oct 07 2014
Sum_{n>1} 1/a(n) = A082832 = 20.569877... (Kempner series).  Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 14 2020


EXAMPLE

22 has no 3s among its digits, hence it is in the sequence.
23 has one 3 among its digits, hence it is not in the sequence.


MAPLE

a:= proc(n) local l, m; l, m:= 0, n1;
while m>0 do l:= (d>
`if`(d<3, d, d+1))(irem(m, 9, 'm')), l
od; parse(cat(l))/10
end:
seq(a(n), n=1..100); # Alois P. Heinz, Aug 01 2016


MATHEMATICA

Select[Range[0, 89], DigitCount[#, 10, 3] == 0 &] (* Alonso del Arte, Oct 16 2012 *)


PROG

(MAGMA) [ n: n in [0..89]  not 3 in Intseq(n) ]; // Bruno Berselli, May 28 2011
(sh) seq 0 1000  grep v 3; # Joerg Arndt, May 29 2011
(PARI)
is(n)=n=digits(n); for(i=1, #n, if(n[i]==3, return(0))); 1 \\ Charles R Greathouse IV, Oct 16 2012
apply( {A052405(n)=fromdigits(apply(d>d+(d>2), digits(n1, 9)))}, [1..99]) \\ a(n)
next_A052405(n, d=digits(n+=1))={for(i=1, #d, d[i]==3&& return((1+n\d=10^(#di))*d)); n} \\ least a(k) > n. Used in A038611. \\ M. F. Hasler, Jan 11 2020
(Haskell)
a052405 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 2 then r + 1 else r where (w, r) = divMod v 9
 Reinhard Zumkeller, Oct 07 2014


CROSSREFS

Cf. A004178, A004722, A038611 (subset of primes), A082832 (Kempner series).
Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).
Cf. A011533 (complement).
Sequence in context: A133016 A026503 A235498 * A039212 A039221 A183297
Adjacent sequences: A052402 A052403 A052404 * A052406 A052407 A052408


KEYWORD

base,easy,nonn


AUTHOR

Henry Bottomley, Mar 13 2000


EXTENSIONS

Offset changed by Reinhard Zumkeller, Oct 07 2014


STATUS

approved



