A004722 Delete all digits 3 from the terms of the sequence of nonnegative integers.

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

Offset

0,3

Comments

Very similar to A004178, except that 3-repdigits (A002277) are completely removed from the sequence, whereas A004178 has 0's in their place. It is thus guaranteed that a(n) = n only when n < 3. - Alonso del Arte, Oct 18 2012

Links

Alonso del Arte, Table of n, a(n) for n = 0..9999

Formula

a(n) = n for -1 < n < 3;

a(n) = A004178(n + 1) for 2 < n < 32,

a(n) = A004178(n + 2) for 31 < n < 331,

a(n) = A004178(n + 3) for 330 < n < 3330,

a(n) = A004178(n + 4) for 3329 < n < 33329, etc. - Alonso del Arte, Oct 21 2012

Mathematica

endAt = 103; Delete[Table[FromDigits[DeleteCases[IntegerDigits[n], 3]], {n, 0, endAt}], Table[{(10^expo - 1)/3 + 1}, {expo, Floor[Log[10, endAt]]}]] (* Alonso del Arte, Apr 29 2019 *)

Prog

(MATLAB) m=1;
for u=0:1000
    v=dec2base(u, 10)-'0'; v = v(v~=3);
    if length(v)>0; sol(m)=(str2num(strrep(num2str(v), ' ', ''))); m=m+1; end;
end
sol % Marius A. Burtea, May 07 2019
(Python)
def A004722(n):
    l = len(str(n))
    m = (10**l-1)//3
    k = n + l - int(n+l < m)
    return 2 if k == m else int(str(k).replace('3', '')) # Chai Wah Wu, Apr 20 2021

Crossrefs

Cf. A004719, A004720, A004721, A004723, A004724, A004725, A004726, A004727, A004728.

Sequence in context: A195994 A182815 A196252 * A094798 A326178 A162880

Adjacent sequences: A004719 A004720 A004721 * A004723 A004724 A004725

Keyword

base,nonn

Author

N. J. A. Sloane

Extensions

Sean A. Irvine pointed out erroneous terms in b-file and confirmed correction, Apr 28 2019

Name edited by Felix Fröhlich, Apr 29 2019

Status

approved