A333237 Numbers k such that 1/k contains at least one '9' in its decimal expansion.
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
Examples
5 is not in the sequence because 1/5 = 0.2 does not contain any 9s.
Links
Crossrefs
Programs
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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 *)
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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
Formula
A333236(a(n)) = 9.
Extensions
More terms from Giovanni Resta, Mar 12 2020
Comments