|
|
A052406
|
|
Numbers without 4 as a digit.
|
|
15
|
|
|
0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
This is a frequent sequence on Chinese, Japanese and Korean elevator buttons. - Jean-Sebastien Girard (circeus(AT)hotmail.com), Jul 28 2008
Essentially numbers in base 9 (using digits 0, 1, 2, 3, 5, 6, 7, 8, 9 rather than 0-8). - Charles R Greathouse IV, Oct 13 2013
|
|
LINKS
|
|
|
FORMULA
|
a(n) = replace digits d > 3 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
|
|
MAPLE
|
a:= proc(n) local l, m; l, m:= 0, n-1;
while m>0 do l:= (d->
`if`(d<4, d, d+1))(irem(m, 9, 'm')), l
od; parse(cat(l))/10
end:
|
|
MATHEMATICA
|
Select[Range[100], DigitCount[#, 10, 4] == 0 &] (* Alonso del Arte, Oct 13 2013 *)
|
|
PROG
|
(PARI) g(n)= local(x, v, j, flag); for(x=1, n, v=Vec(Str(x)); flag=1; for(j=1, length(v), if(v[j]=="4", flag=0)); if(flag, print1(x", ") ) ) \\ Cino Hilliard, Apr 01 2007
(PARI)
apply( {A052406(n)=fromdigits(apply(d->d+(d>3), digits(n-1, 9)))}, [1..99]) \\ a(n)
select( {is_A052406(n)=!setsearch(Set(digits(n)), 4)}, [0..99]) \\ Used in A038612
next_A052406(n, d=digits(n+=1))={for(i=1, #d, d[i]!=4|| return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used for A038612. - M. F. Hasler, Jan 11 2020
(Magma) [ n: n in [0..89] | not 4 in Intseq(n) ]; // Bruno Berselli, May 28 2011
(sh) seq 0 1000 | grep -v 4; # Joerg Arndt, May 29 2011
(Haskell)
a052406 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 3 then r + 1 else r where (w, r) = divMod v 9
(Python) def A052406(n): n-=1; return sum((d+(d>3))*10**i for d, i in ((n//9**i%9, i) for i in range(math.ceil(math.log(n+1, 9))))) # M. F. Hasler, Jan 13 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|