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A052413
Numbers without 5 as a digit.
17
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, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89
OFFSET
1,3
FORMULA
a(n) = replace digits d > 4 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
Sum_{k>1} 1/a(n) = A082834 = 21.8346008... (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<5, 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], !MemberQ[IntegerDigits[#], 5]&] (* Harvey P. Dale, Feb 20 2013 *)
PROG
(Magma) [ n: n in [0..89] | not 5 in Intseq(n) ]; // Bruno Berselli, May 28 2011
(sh) seq 0 1000 | grep -v 5; # Joerg Arndt, May 29 2011
(Haskell)
a052413 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 4 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014
(PARI)
apply( {A052413(n)=fromdigits(apply(d->d+(d>4), digits(n-1, 9)))}, [1..99]) \\ a(n)
select( {is_A052413(n)=!setsearch(Set(digits(n)), 5)}, [0..99]) \\ used in A038613
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
(Python) # see the OEIS wiki page (cf. LINKS) for more programs
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
CROSSREFS
Cf. A004180, A004724, A038613 (subset of primes), A082834 (Kempner series).
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).
Sequence in context: A340288 A132329 A230313 * A276389 A302058 A183302
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Mar 13 2000
EXTENSIONS
Offset changed by Reinhard Zumkeller, Oct 07 2014
STATUS
approved