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

1,1

Comments

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}.

Links

Table of n, a(n) for n=1..51.

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

Example

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

Mathematica

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

Prog

(Python)
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<<m2)//5**m5)-1
        if max(max(str(c:=k//a)), max(str(m*k//a-c*m)))=='7':
            yield a
A351473_list = list(islice(A351473_gen(), 20)) # Chai Wah Wu, May 02 2023

Crossrefs

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.

Sequence in context: A326893 A160119 A160379 * A152053 A166649 A025145

Adjacent sequences: A351470 A351471 A351472 * A351474 A351475 A351476

Keyword

nonn,base

Author

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

Status

approved