

A052405


Numbers without 3 as a digit.


17



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



FORMULA

a(n) = replace digits d > 2 by d + 1 in base9 representation of n  1.  Reinhard Zumkeller, Oct 07 2014


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:


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)
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


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



