A052413 - OEIS

%I #48 Sep 08 2022 08:44:59

%S 0,1,2,3,4,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,26,27,28,

%T 29,30,31,32,33,34,36,37,38,39,40,41,42,43,44,46,47,48,49,60,61,62,63,

%U 64,66,67,68,69,70,71,72,73,74,76,77,78,79,80,81,82,83,84,86,87,88,89

%N Numbers without 5 as a digit.

%H Reinhard Zumkeller, <a href="/A052413/b052413.txt">Table of n, a(n) for n = 1..10000</a>

%H M. F. Hasler, <a href="/wiki/Numbers_avoiding_certain_digits">Numbers avoiding certain digits</a>, OEIS wiki, Jan 12 2020

%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.

%F a(n) = replace digits d > 4 by d + 1 in base-9 representation of n - 1. - _Reinhard Zumkeller_, Oct 07 2014

%F Sum_{k>1} 1/a(n) = A082834 = 21.8346008... (Kempner series). - _Bernard Schott_, Jan 12 2020, edited by _M. F. Hasler_, Jan 13 2020

%p a:= proc(n) local l, m; l, m:= 0, n-1;

%p       while m>0 do l:= (d->

%p         `if`(d<5, d, d+1))(irem(m, 9, 'm')), l

%p       od; parse(cat(l))/10

%p     end:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 01 2016

%t Select[Range[100],!MemberQ[IntegerDigits[#],5]&] (* _Harvey P. Dale_, Feb 20 2013 *)

%o (Magma) [ n: n in [0..89] | not 5 in Intseq(n) ]; // _Bruno Berselli_, May 28 2011

%o (sh) seq 0 1000 | grep -v 5; # _Joerg Arndt_, May 29 2011

%o (Haskell)

%o a052413 = f . subtract 1 where

%o f 0 = 0

%o f v = 10 * f w + if r > 4 then r + 1 else r where (w, r) = divMod v 9

%o -- _Reinhard Zumkeller_, Oct 07 2014

%o (PARI)

%o apply( {A052413(n)=fromdigits(apply(d->d+(d>4),digits(n-1,9)))}, [1..99]) \\ a(n)

%o select( {is_A052413(n)=!setsearch(Set(digits(n)),5)}, [0..99]) \\ used in A038613

%o next_A052413(n, d=digits(n+=1))={for(i=1,#d, d[i]==5&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n; used in A038613. - _M. F. Hasler_, Jan 11 2020

%o (Python) # see the OEIS wiki page (cf. LINKS) for more programs

%o def A052413(n): n-=1; return sum(n//9**e%9*6//5*10**e for e in range(math.ceil(math.log(n+1,9)))) # _M. F. Hasler_, Jan 13 2020

%Y Cf. A004180, A004724, A038613 (subset of primes), A082834 (Kempner series).

%Y Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

%K base,easy,nonn

%O 1,3

%A _Henry Bottomley_, Mar 13 2000

%E Offset changed by _Reinhard Zumkeller_, Oct 07 2014