|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
LINKS
|
|
|
FORMULA
|
|
|
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:
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|