A333402 -id:A333402 - cp's OEIS frontend

A351473 Numbers m such that the largest digit in the decimal expansion of 1/m is 7.

27, 36, 37, 44, 132, 135, 148, 234, 270, 288, 292, 297, 308, 315, 360, 364, 369, 370, 404, 407, 440, 468, 576, 616, 636, 657, 707, 728, 756, 808, 864, 1287, 1295, 1313, 1314, 1320, 1332, 1350, 1365, 1375, 1386, 1404, 1408, 1476, 1480, 1485, 1507, 1512, 1752, 1804, 1896

Offset: 1

Bernard Schott and Robert G. Wilson v, Feb 17 2022

If k is a term, 10*k is also a term.
First few primitive terms are 27, 36, 37, 44, 132, 135, 148, 234, 288, ...
The unique prime up to 2.6*10^8 is 37 (see comments in A333237 and example).
Subsequence: {132, 1332, 13332, ...} = A073551 \ {2, 12}.

			As 1/37 = 0.027027027..., 37 is a term.
As 1/148 = 0.00675675675675..., 148 is a term.

Index entries for sequences related to decimal expansion of 1/n.

Similar with largest digit k: A333402 (k=1), A341383 (k=2), A350814 (k=3), A351470 (k=4), A351471 (k=5), A351472 (k=6), this sequence (k=7), A351474 (k=8), A333237 (k=9).

Cf. A073551, A333236.

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[Range@1500000, Max@ f@# == 7 &]

from itertools import count, islice
from sympy import multiplicity, n_order
def A351473_gen(startvalue=1): # generator of terms >= startvalue
    for a in count(max(startvalue,1)):
        m2, m5 = (~a&a-1).bit_length(), multiplicity(5,a)
        k, m = 10**max(m2,m5), 10**n_order(10,a//(1<A351473_list = list(islice(A351473_gen(),20)) # Chai Wah Wu, May 02 2023

A333607 Numbers k with unique nonzero digit in decimal representation of 1/k.

Original entry on oeis.org

1, 2, 3, 5, 9, 10, 11, 15, 18, 20, 25, 30, 33, 45, 50, 90, 99, 100, 101, 110, 111, 125, 150, 165, 180, 198, 200, 225, 250, 300, 303, 330, 333, 450, 495, 500, 900, 909, 990, 999, 1000, 1001, 1010, 1100, 1110, 1111, 1125, 1250, 1287, 1500, 1515, 1650, 1665, 1800

Offset: 1

Rémy Sigrist, Mar 28 2020

This sequence has similarities with A125289; here we consider the decimal representation of 1/n, there that of n.
This sequence contains A333402.
If m belongs to the sequence, then 10*m also belongs to the sequence.

			The first terms, alongside their inverse, are:
  n   a(n)  1/a(n)
  --  ----  -----------
   1     1  1
   2     2  0.5
   3     3  0.333333...
   4     5  0.2
   5     9  0.111111...
   6    10  0.1
   7    11  0.090909...
   8    15  0.066666...
   9    18  0.055555...
  10    20  0.05
  11    25  0.04
  12    30  0.033333...
  13    33  0.030303...

Rémy Sigrist, PARI program for A333607

Cf. A125289, A333402.

PARI
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See Links section.
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A343506 Numbers k such that the largest digit in the factorial base expansion of 1/k is 1.

Original entry on oeis.org

1, 2, 6, 20, 24, 120, 630, 720, 4480, 5040, 36288, 40320, 362880, 3326400, 3628800, 39916800

Offset: 1

Rémy Sigrist, Apr 17 2021

Equivalently these are the numbers k such that A299020(k) = 1 or A343505(k) = 1.
This sequence is infinite as it contains:
- the factorial numbers (A000142),
- 1/(1/A060462(k)! + 1/(A060462(k)-1)!) for k > 2,
- 1/(1/A120416(k)! + 1/(A120416(k)-1)! + 1/(A120416(k)-2)!) for k > 0.

			The first terms, alongside the factorial base expansion of their inverse, are:
  n   a(n)     1/a(n) in factorial base
  --  -------  ------------------------
   1        1  1
   2        2  0.1
   3        6  0.0 1
   4       20  0.0 0 1 1
   5       24  0.0 0 1
   6      120  0.0 0 0 1
   7      630  0.0 0 0 0 1 1
   8      720  0.0 0 0 0 1
   9     4480  0.0 0 0 0 0 1 1
  10     5040  0.0 0 0 0 0 1
  11    36288  0.0 0 0 0 0 0 1 1
  12    40320  0.0 0 0 0 0 0 1
  13   362880  0.0 0 0 0 0 0 0 1
  14  3326400  0.0 0 0 0 0 0 0 0 1 1
  15  3628800  0.0 0 0 0 0 0 0 0 1

Cf. A000142, A060462, A120416, A294168, A299020, A343505.

Cf. A333402 (decimal).

is(n) = my (f=1/n); for (r=2, oo, if (f==0, return (1), floor(f)>1, return (0), f=frac(f)*r))

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A351473 Numbers m such that the largest digit in the decimal expansion of 1/m is 7.

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A333607 Numbers k with unique nonzero digit in decimal representation of 1/k.

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A343506 Numbers k such that the largest digit in the factorial base expansion of 1/k is 1.

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PARI