A052421 Numbers without 8 as a digit.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020.

Index entries for 10-automatic sequences.

Formula

a(n) = replace digits d > 7 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{n>1} 1/a(n) = A082837 = 22.726365... (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<8, 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[0, 100], DigitCount[#, 10, 8]==0&] (* Harvey P. Dale, Oct 11 2012 *)

Prog

(Magma) [ n: n in [0..89] | not 8 in Intseq(n) ]; // Bruno Berselli, May 28 2011
(sh) seq 0 1000 | grep -v 8; # Joerg Arndt, May 29 2011
(Haskell)
a052421 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 7 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014
(PARI) lista(nn)=for (n=0, nn, if (!vecsearch(vecsort(digits(n), , 8), 8), print1(n, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI) /* See OEIS wiki page (cf. LINKS) for more programs. */
apply( {A052421(n)=fromdigits(apply(d->d+(d>7), digits(n-1, 9)))}, [1..99]) \\ a(n)
select( {is_A052421(n)=!setsearch(Set(digits(n)), 8)}, [0..99]) \\ used in A038616
next_A052421(n, d=digits(n+=1))={for(i=1, #d, d[i]==8&&return((1+n\d=10^(#d-i))*d)); n} \\ Least a(k) > n. Used in A038616. - M. F. Hasler, Jan 11 2020

Crossrefs

Cf. A004183, A004727, A038616 (subset of primes), A082837 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A007095 (without 9).

Sequence in context: A242094 A349144 A171524 * A248375 A037477 A277050

Adjacent sequences: A052418 A052419 A052420 * A052422 A052423 A052424

Keyword

base,easy,nonn

Author

Henry Bottomley, Mar 13 2000

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014

Status

approved