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A350814
Numbers m such that the largest digit in the decimal expansion of 1/m is 3.
8
3, 30, 33, 75, 300, 303, 330, 333, 429, 750, 813, 3000, 3003, 3030, 3125, 3300, 3330, 3333, 4290, 4329, 7500, 7575, 8130, 30000, 30003, 30030, 30300, 30303, 31250, 33000, 33300, 33330, 33333, 42900, 43290, 46875, 75000, 75075, 75750, 76923, 81103, 81300, 300000
OFFSET
1,1
COMMENTS
If m is a term, 10*m is also a term.
3 is the only prime up to 2.6*10^8 (see comments in A333237).
Some subsequences:
{3, 30, 300, ...} = A093138 \ {1}.
{3, 33, 333, ...} = A002277 \ {0}.
{3, 33, 303, 3003, ...} = 3 * A000533.
{3, 303, 30303, 3030303, ...} = 3 * A094028.
EXAMPLE
As 1/33 = 0.0303030303..., 33 is a term.
As 1/75 = 0.0133333333..., 75 is a term.
As 1/429 = 0.002331002331002331..., 429 is a term.
MATHEMATICA
Select[Range[10^5], Max[RealDigits[1/#][[1]]] == 3 &] (* Amiram Eldar, Jan 30 2022 *)
PROG
(Python)
from fractions import Fraction
from itertools import count, islice
from sympy import n_order, multiplicity
def repeating_decimals_expr(f, digits_only=False):
""" returns repeating decimals of Fraction f as the string aaa.bbb[ccc].
returns only digits if digits_only=True.
"""
a, b = f.as_integer_ratio()
m2, m5 = multiplicity(2, b), multiplicity(5, b)
r = max(m2, m5)
k, m = 10**r, 10**n_order(10, b//2**m2//5**m5)-1
c = k*a//b
s = str(c).zfill(r)
if digits_only:
return s+str(m*k*a//b-c*m)
else:
w = len(s)-r
return s[:w]+'.'+s[w:]+'['+str(m*k*a//b-c*m)+']'
def A350814_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda m:max(repeating_decimals_expr(Fraction(1, m), digits_only=True)) == '3', count(max(startvalue, 1)))
A350814_list = list(islice(A350814_gen(), 10)) # Chai Wah Wu, Feb 07 2022
CROSSREFS
Similar with largest digit k: A333402 (k=1), A341383 (k=2), A333237 (k=9).
Subsequences: A002277 \ {0}, A093138 \ {1}.
Decimal expansion: A010701 (1/3), A010674 (1/33).
Sequence in context: A045863 A121023 A124520 * A169966 A140153 A095045
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jan 30 2022
EXTENSIONS
More terms from Amiram Eldar, Jan 30 2022
STATUS
approved