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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
M. F. Hasler, Numbers avoiding certain digits OEIS wiki, Jan 12 2020.
Eric Weisstein's World of Mathematics, Uban Number
Wikipedia, Tetraphobia.
FORMULA
a(n) = replace digits d > 3 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
Sum_{k>1} 1/a(k) = A082833 = 21.327465... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 13 2020
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:
seq(a(n), n=1..100); # Alois P. Heinz, Aug 01 2016
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
-- Reinhard Zumkeller, Oct 07 2014
(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
Cf. A004179, A004723, A011760, A038612 (subset of primes), A082833 (Kempner series).
Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).
Sequence in context: A258022 A333638 A089590 * A022306 A183298 A081023
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Mar 13 2000
EXTENSIONS
Offset changed by Reinhard Zumkeller, Oct 07 2014
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)