A004724 Delete all 5's from the sequence of nonnegative integers.

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 16, 17, 18, 19, 20, 21, 22, 23, 24, 2, 26, 27, 28, 29, 30, 31, 32, 33, 34, 3, 36, 37, 38, 39, 40, 41, 42, 43, 44, 4, 46, 47, 48, 49, 0, 1, 2, 3, 4, 6, 7, 8, 9, 60, 61, 62, 63, 64, 6, 66, 67, 68, 69, 70, 71, 72, 73, 74, 7, 76

Offset

0,3

Comments

In contrast to the variant A004180 where a(n) = 0 when all the digits of n are 5's, here a number completely disappears in that case, so that subsequent indices are shifted and for n > 4, a(n) is not the result of deleting 5's from n: see formula. - M. F. Hasler, Jan 13 2020

Links

Table of n, a(n) for n=0..74.

Formula

a(n) = A004180(n + m) where m = L(n) - [ (10^L(n)-1)/9*5 >= n + L(n) ], L(n) = floor(log_10(max(n,1)) + 1), the number of digits of n, and [...] is the Iverson bracket (1 if true, 0 else). - M. F. Hasler, Jan 13 2020

Example

From  M. F. Hasler, Jan 13 2020: (Start)
After a(4) = 4 comes a(5) = 6, since the number 5 completely disappears.
a(48) = 49 is followed by 0, 1, 2, 3, 4 (i.e., 50, ..., 54 with the initial digit removed) and then a(54) = 6, because 55 disappears completely.
Illustration of the formula: as long as n < 5 (the first number that completely disappears) we have a(n) = A004180(n). Here n has 1 digit but n+1 does not exceed the (single repdigit) 5 (left hand side in the Iverson bracket), so m = 0. From n = 5 on, n+1 > 5, so m = 1.
Then, when n has L(n) = 2 digits, we still have n = 2 - 1 = 1 as long as n+2 <= 55 or n <= 53, but m = 3 for n > 55 - 2 = 53, i.e., from n = 54 on (where the term 55 has disappeared, see above).
Similarly, m = 3 for n > 555 - 3, i.e., from n >= 553 on, etc. (End)

Prog

(PARI)
apply( {A004724(n, L=logint(n+!n, 10)+1)=A004180(n+L-(10^L\9*5-L>=n))}, [0..99])
A004724_upto(N)={[fromdigits(v)|v<-[[d|d<-digits(n+!n*50), d!=5]|n<-[0..N]], #v]} \\ M. F. Hasler, Jan 13 2020
(MATLAB) m=1; for u=0:76 v=dec2base(u, 10)-'0'; v = v(v~=5);  if length(v)>0; sol(m)=(str2num(strrep(num2str(v), ' ', ''))); m=m+1; end; end; sol % Marius A. Burtea, Jan 16 2020
(Python)
def A004724(n):
    l = len(str(n))
    m = 5*(10**l-1)//9
    k = n + l - int(n+l < m)
    return 4 if k == m else int(str(k).replace('5', '')) # Chai Wah Wu, Apr 20 2021

Crossrefs

Cf. A004180 (delete digits 5 in n), A052413 (numbers with no digit 5).

Cf. A004719, A004720, A004721, A004722, A004723, A004725, A004726, A004727, A004728.

Sequence in context: A366429 A071789 A131870 * A099260 A231237 A053241

Adjacent sequences: A004721 A004722 A004723 * A004725 A004726 A004727

Keyword

base,nonn

Author

N. J. A. Sloane

Status

approved