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A052414
Numbers without 6 as a digit.
16
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
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
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Mar 13 2000
EXTENSIONS
Offset changed by Reinhard Zumkeller, Oct 07 2014
STATUS
approved