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%I #30 May 02 2023 14:40:20
%S 7,12,14,26,28,35,48,54,55,56,63,65,70,72,78,79,93,117,120,123,125,
%T 128,140,175,176,186,192,195,205,224,239,259,260,264,280,296,312,318,
%U 328,350,372,416,432,438,448,465,480,540,542,546,548,550,555,560,572,584,594,630,632,650,675
%N Numbers m such that the largest digit in the decimal expansion of 1/m is 8.
%C 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, ...
%C 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).
%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>.
%F A333236(a(n)) = 8.
%e As 1/7 = 0.142857142857142857..., 7 is a term.
%e As 1/26 = 0.0384615384615384615..., 26 is another term.
%t f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[Range@1500000, Max@ f@# == 8 &]
%o (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
%o (Python)
%o from itertools import count, islice
%o from sympy import multiplicity, n_order
%o def A351474_gen(startvalue=1): # generator of terms >= startvalue
%o for a in count(max(startvalue,1)):
%o m2, m5 = (~a&a-1).bit_length(), multiplicity(5,a)
%o k, m = 10**max(m2,m5), 10**n_order(10,a//(1<<m2)//5**m5)-1
%o if max(max(str(c:=k//a)),max(str(m*k//a-c*m)))=='8':
%o yield a
%o A351474_list = list(islice(A351474_gen(),20)) # _Chai Wah Wu_, May 02 2023
%Y 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).
%Y Cf. A333236.
%Y Decimal expansion of: A020806 (1/7), A021058 (1/54), A021060 (1/56), A021067 (1/63), A021069 (1/65), A021083 (1/79), A021097 (1/93).
%K nonn,base
%O 1,1
%A _Bernard Schott_ and _Robert G. Wilson v_, Feb 19 2022
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