A021058 -id:A021058 - cp's OEIS frontend

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

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

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).

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

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

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

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<A351474_list = list(islice(A351474_gen(),20)) # Chai Wah Wu, May 02 2023

A333236(a(n)) = 8.

A355183 Decimal expansion of the area of the region that represents the set of points in a unit square that are closer to the center of the square than to the closest edge.

Original entry on oeis.org

2, 1, 8, 9, 5, 1, 4, 1, 6, 4, 9, 7, 4, 6, 0, 0, 6, 5, 0, 6, 8, 9, 1, 8, 2, 9, 8, 9, 4, 6, 2, 6, 4, 1, 0, 4, 7, 5, 9, 5, 6, 2, 5, 0, 0, 5, 0, 2, 5, 9, 7, 4, 3, 0, 9, 0, 2, 2, 3, 9, 6, 5, 0, 6, 5, 4, 3, 0, 9, 9, 7, 1, 2, 8, 2, 8, 0, 9, 3, 8, 5, 1, 3, 3, 8, 5, 0, 0, 4, 5, 7, 7, 0, 1, 8, 8, 7, 6, 3, 6, 4, 6, 6, 8, 5

Offset: 0

Amiram Eldar, Jun 23 2022

The shape is formed by the intersection of four parabolas. Its perimeter is given in A355184.

			0.21895141649746006506891829894626410475956250050259...

Kiran S. Kedlaya, Bjorn Poonen, and Ravi Vakil, The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary, The Mathematical Association of America, 2002, pp. 108-109.

Joel Atkins, Regular Polygon Targets, Pi Mu Epsilon Journal, Vol. 9, No. 3 (1989), pp. 142-144; entire issue.
Nicholas R. Baeth, Loren Luther, and Rhonda McKee, The Downtown Problem: Variations on a Putnam Problem, Mathematics Magazine, Vol. 90, No. 4 (2017), pp. 243-257.
John Coffey, Q19, Maths Puzzles & Problems, MathStudio, 2011.
Amiram Eldar, Illustration.
Leonard F. Klosinski, Gerald L. Alexanderson, and Loren C. Larson, The Fiftieth William Lowell Putnam Mathematical Competition, The American Mathematical Monthly, Vol. 98, No. 4 (1991), pp. 319-327.
Missouri State University, Problem #5, The Area and Perimeter of a Certain Region, Advanced Problem Archive; Solution to Problem #5, by John Shonder.
Jun-Ping Shi, Problem Set 9.

Cf. A021058, A103712, A244921, A254140, A352453, A355184 (perimeter), A355185 (3D analog).

RealDigits[(4*Sqrt[2] - 5)/3, 10, 100][[1]]

Equals (4*sqrt(2)-5)/3.

A261882 Decimal expansion of 32/27.

Original entry on oeis.org

1, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5, 1, 8, 5

Offset: 1

Charles R Greathouse IV, Sep 04 2015

For any number x >= 32/27 and any e > 0, there is a graph G such that the chromatic polynomial of G has a real root between x - e and x + e. (All real roots of such polynomials are 0, 1, or in this range.)
Continued fraction expansion of (sqrt(730)-10)/9. - Bruno Berselli, Sep 04 2015
Periodic (beyond the first term) with period 3. - Charles R Greathouse IV, Sep 05 2015
Equals the ratio of the wavelengths between the hydrogen spectral lines Lyman-alpha (121.6 nm) and Lyman-beta (102.6 nm). - Sean Stroud, Apr 15 2019

			1.18518518518518518...

Peter J. Cameron's Blog, Algebraic properties of chromatic roots, Oct 04 2016.
Bill Jackson, A zero-free interval for chromatic polynomials of graphs, Combinatorics, Probability and Computing 2:3 (Sept 1993), pp. 325-336.
Bill Jackson and Alan Sokal, Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and matroids, J. Combin. Theory Ser. B 99:6 (2009), pp. 869-903.
Carsten Thomassen, The zero-free intervals for chromatic polynomials of graphs, Combin. Probab. Comput. 6:4 (1997), pp. 497-506.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 1).

Cf. A021058.

Digits := 100; evalf(32/27); # Wesley Ivan Hurt, Sep 04 2015

First@ RealDigits[N[32/27, 120]] (* Michael De Vlieger, Sep 04 2015 *)
Join[{1}, Table[7 - (-1)^Mod[n - 1, 3]/2 - 5 (-1)^Mod[n, 3]/2 - 4 (-1)^Mod[n + 1, 3], {n, 2, 40}]] (* Wesley Ivan Hurt, Sep 04 2015 *)

PARI
```
32/27.
```

G.f.: x*(1 + x + 8*x^2 + 4*x^3)/((1 - x)*(1 + x + x^2)). - Bruno Berselli, Sep 04 2015

a(n) = 7-(-1)^(n-1 mod 3)/2-5*(-1)^(n mod 3)/2-4*(-1)^(n+1 mod 3), n>1. - Wesley Ivan Hurt, Sep 04 2015

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

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A355183 Decimal expansion of the area of the region that represents the set of points in a unit square that are closer to the center of the square than to the closest edge.

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A261882 Decimal expansion of 32/27.

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