A350814 Numbers m such that the largest digit in the decimal expansion of 1/m is 3.
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
Examples
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.
Crossrefs
Programs
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Mathematica
Select[Range[10^5], Max[RealDigits[1/#][[1]]] == 3 &] (* Amiram Eldar, Jan 30 2022 *)
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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
Extensions
More terms from Amiram Eldar, Jan 30 2022
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