|
| |
|
|
A052383
|
|
Numbers without 1 as a digit.
|
|
29
|
|
|
|
0, 2, 3, 4, 5, 6, 7, 8, 9, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
For each k in {1, 2, ..., 29, 30, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43} there exists at least an m such that m^k is 1-less. If m^k is 1-less then (10*m)^k, (100*m)^k, (1000*m)^k, ... are also 1-less. Therefore for each of these numbers k there exist infinitely many k-th powers in this sequence. - Mohammed Yaseen, Apr 17 2023
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(1) = 1, a(n + 1) = f(a(n) + 1, a(n) + 1) where f(x, y) = if x < 10 and x <> 1 then y else if x mod 10 = 1 then f(y + 1, y + 1) else f(floor(x/10), y). - Reinhard Zumkeller, Mar 02 2008
a(n) is the replacement of all nonzero digits d by d + 1 in the base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
|
|
|
MAPLE
|
M:= 3: # to get all terms with up to M digits
B:= {$2..9}: A:= B union {0}:
for m from 1 to M do
B:= map(b -> seq(10*b+j, j={0, $2..9}), B);
A:= A union B;
od:
# second program:
option remember;
if n = 1 then
0;
else
for a from procname(n-1)+1 do
if nops(convert(convert(a, base, 10), set) intersect {1}) = 0 then
return a;
end if;
end do:
end if;
# third Maple program:
a:= proc(n) local l, m; l, m:= 0, n-1;
while m>0 do l:= (d->
`if`(d=0, 0, d+1))(irem(m, 9, 'm')), l
od; parse(cat(l))/10
end:
|
|
|
MATHEMATICA
|
ban1Q[n_] := FreeQ[IntegerDigits[n], 1] == True; Select[Range[0, 89], ban1Q[#] &] (* Jayanta Basu, May 17 2013 *)
Select[Range[0, 99], DigitCount[#, 10, 1] == 0 &] (* Alonso del Arte, Jan 12 2020 *)
|
|
|
PROG
|
(Magma) [ n: n in [0..89] | not 1 in Intseq(n) ]; // Bruno Berselli, May 28 2011
(sh) seq 0 1000 | grep -v 1; # Joerg Arndt, May 29 2011
(PARI) a(n)=my(v=digits(n, 9)); for(i=1, #v, if(v[i], v[i]++)); subst(Pol(v), 'x, 10) \\ Charles R Greathouse IV, Oct 04 2012
(PARI)
apply( {A052383(n)=fromdigits(apply(d->d+!!d, digits(n-1, 9)))}, [1..99]) \\ Defines the function and computes it for indices 1..99 (check & illustration)
select( {is_A052383(n)=!setsearch(Set(digits(n)), 1)}, [0..99]) \\ Define the characteristic function is_A; as illustration, select the terms in [0..99]
next_A052383(n, d=digits(n+=1))={for(i=1, #d, d[i]==1&& return((1+n\d=10^(#d-i))*d)); n} \\ Successor function: efficiently skip to the next a(k) > n. Used in A038603. - M. F. Hasler, Jan 11 2020
(Haskell)
a052383 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 0 then r + 1 else 0 where (w, r) = divMod v 9
(Scala) (0 to 99).filter(_.toString.indexOf('1') == -1) // Alonso del Arte, Jan 12 2020
(Python)
from itertools import count, islice, product
def A052383(): # generator of terms
yield 0
for digits in count(1):
for f in "23456789":
for r in product("023456789", repeat=digits-1):
yield int(f+"".join(r))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
base,easy,nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
