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A333237
Numbers k such that 1/k contains at least one '9' in its decimal expansion.
20
11, 13, 17, 19, 21, 23, 29, 31, 34, 38, 41, 42, 43, 46, 47, 49, 51, 52, 53, 57, 58, 59, 61, 62, 67, 68, 69, 71, 73, 76, 77, 81, 82, 83, 84, 85, 86, 87, 89, 91, 92, 94, 95, 97, 98, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118
OFFSET
1,1
COMMENTS
Almost every prime appears in this sequence.
Among the first 10000 primes, only 2, 3, 5, 7, 37, 79, 239, 4649, and 62003 do not appear in the sequence. - Giovanni Resta, Mar 13 2020
The next primes not in the sequence are 538987, 35121409, and 265371653. - Robert Israel, Mar 18 2020
FORMULA
A333236(a(n)) = 9.
EXAMPLE
5 is not in the sequence because 1/5 = 0.2 does not contain any 9s.
MAPLE
f:= proc(n) local m, S, r;
m:= 1; S:= {1};
do
r:= floor(m/n);
if r = 9 then return true fi;
m:= (m - r*n)*10;
if member(m, S) then return false fi;
S:= S union {m};
od
end proc:
select(f, [$1..1000]); # Robert Israel, Mar 18 2020
MATHEMATICA
Select[Range[120], MemberQ[ Flatten@ RealDigits[1/#][[1]], 9] &] (* Giovanni Resta, Mar 12 2020 *)
PROG
(Python)
from itertools import count, islice
from sympy import n_order, multiplicity
def A333237_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if max(str(10**(max(m2, m5)+n_order(10, m//2**m2//5**m5))//m)) == '9':
yield m
A333237_list = list(islice(A333237_gen(), 10)) # Chai Wah Wu, Feb 07 2022
CROSSREFS
Cf. A333236.
Subsequences (for terms > 1): A000533, A002275, A135577, A252491.
Cf. A216664 (a subsequence).
Cf. A187614.
Sequence in context: A352154 A138708 A061116 * A048388 A068191 A191599
KEYWORD
nonn,base,easy
AUTHOR
Andrew Slattery, Mar 12 2020
EXTENSIONS
More terms from Giovanni Resta, Mar 12 2020
STATUS
approved