A052414 Numbers without 6 as a digit.

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89

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 > 5 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{k>1} 1/a(k) = A082835 = 22.205598... (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<6, 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, 6]==0&] (* Harvey P. Dale, Jun 20 2013 *)

Prog

(Magma) [ n: n in [0..89] | not 6 in Intseq(n) ]; // Bruno Berselli, May 28 2011
(sh) seq 0 1000 | grep -v 6; # Joerg Arndt, May 29 2011
(Haskell)
a052414 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 5 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), 6), print1(n, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI) /* See OEIS wiki page (cf. LINKS) for more programs */
apply( {A052414(n)=fromdigits(apply(d->d+(d>5), digits(n-1, 9)))}, [1..99]) \\ a(n)
select( {is_A052414(n)=!setsearch(Set(digits(n)), 6)}, [0..99]) \\ used in A038614
next_A052414(n, d=digits(n+=1))={for(i=1, #d, d[i]==6&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n, used in A038614. - M. F. Hasler, Jan 11 2020

Crossrefs

Cf. A004181, A004725, A038614 (subset of primes), A082835 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052419 (without 7), A052421 (without 8), A007095 (without 9).

Sequence in context: A029916 A175407 A232490 * A095410 A022293 A183218

Adjacent sequences: A052411 A052412 A052413 * A052415 A052416 A052417

Keyword

base,easy,nonn

Author

Henry Bottomley, Mar 13 2000

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014

Status

approved