A351474 Numbers m such that the largest digit in the decimal expansion of 1/m is 8.

7, 12, 14, 26, 28, 35, 48, 54, 55, 56, 63, 65, 70, 72, 78, 79, 93, 117, 120, 123, 125, 128, 140, 175, 176, 186, 192, 195, 205, 224, 239, 259, 260, 264, 280, 296, 312, 318, 328, 350, 372, 416, 432, 438, 448, 465, 480, 540, 542, 546, 548, 550, 555, 560, 572, 584, 594, 630, 632, 650, 675

Offset

1,1

Comments

If k is a term, 10*k is also a term. First few primitive terms are 7, 12, 14, 26, 28, 35, 48, 54, 55, 56, 63, 65, 72, ...

The seven primes up to 2.7*10^8 are 7, 79, 239, 62003, 538987, 35121409, 265371653 (see comments in A333237, example section and Crossrefs).

Links

Table of n, a(n) for n=1..61.

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

Formula

A333236(a(n)) = 8.

Example

As 1/7 = 0.142857142857142857..., 7 is a term.
As 1/26 = 0.0384615384615384615..., 26 is another term.

Mathematica

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[Range@1500000, Max@ f@# == 8 &]

Prog

(PARI) isok(m) = my(m2=valuation(m, 2), m5=valuation(m, 5)); vecmax(digits(floor(10^(max(m2, m5) + znorder(Mod(10, m/2^m2/5^m5))+1)/m))) == 8; \\ Michel Marcus, Feb 26 2022
(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A351474_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)))=='8':
            yield a
A351474_list = list(islice(A351474_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), A351473 (k=7), this sequence (k=8), A333237 (k=9).

Cf. A333236.

Decimal expansion of: A020806 (1/7), A021058 (1/54), A021060 (1/56), A021067 (1/63), A021069 (1/65), A021083 (1/79), A021097 (1/93).

Sequence in context: A062730 A287562 A341092 * A349854 A073255 A162194

Adjacent sequences: A351471 A351472 A351473 * A351475 A351476 A351477

Keyword

nonn,base

Author

Bernard Schott and Robert G. Wilson v, Feb 19 2022

Status

approved