A052419 Numbers without 7 as a digit.

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 80, 81, 82, 83, 84, 85, 86, 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 > 6 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{n>1} 1/a(n) = A082836 = 22.493475... (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<7, 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, 7]==0&] (* Harvey P. Dale, Aug 23 2011 *)

Prog

(Magma) [ n: n in [0..89] | not 7 in Intseq(n) ]; // Bruno Berselli, May 28 2011
(sh) seq 0 1000 | grep -v 7; # Joerg Arndt, May 29 2011
(Haskell)
a052419 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 6 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), 7), print1(n, ", ")); ); \\ Michel Marcus, Feb 22 2015
(PARI) /* See OEIS wiki page for more programs. */
apply( {A052419(n)=fromdigits(apply(d->d+(d>6), digits(n-1, 9)))}, [1..99]) \\ a(n)
select( {is_A052419(n)=!setsearch(Set(digits(n)), 7)}, [0..99]) \\ used in A038615
next_A052419(n, d=digits(n+=1))={for(i=1, #d, d[i]==7&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used in A038615. - M. F. Hasler, Jan 11 2020
(Python)
from gmpy2 import digits
def A052419(n): return int(digits(n-1, 9).replace('8', '9').replace('7', '8')) # Chai Wah Wu, Jun 28 2025

Crossrefs

Cf. A004182, A004726, A038615 (subset of primes), A082836 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052421 (without 8), A007095 (without 9).

Sequence in context: A183219 A049533 A383031 * A257458 A179439 A047421

Adjacent sequences: A052416 A052417 A052418 * A052420 A052421 A052422

Keyword

base,easy,nonn

Author

Henry Bottomley, Mar 13 2000

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014

Status

approved