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Integers m such that the decimal expansion of 1/m contains the digit 3.
7

%I #12 Jul 01 2023 16:54:07

%S 3,12,13,17,19,23,26,27,28,29,30,31,32,33,34,38,41,42,43,46,47,48,49,

%T 51,52,53,57,58,59,61,62,63,65,67,68,69,71,72,73,74,75,76,81,83,85,87,

%U 88,89,92,93,94,95,97,98,102,103,104,105,106,107,109,113,114,115,116

%N Integers m such that the decimal expansion of 1/m contains the digit 3.

%C If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.

%e m = 12 is a term since 1/12 = 0.083333333333... (here, 3 is the smallest digit).

%e m = 13 is a term since 1/13 = 0.076923076923...

%e m = 75 is a term since 1/15 = 0.013333333333... (here, 3 is the largest digit).

%t f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 125, MemberQ[f@#, 3] &]

%Y A350814 (largest digit=3) and A352157 (smallest digit=3) are subsequences.

%Y Similar with digit k: A352154 (k=0), A353437 (k=1), A353438 (k=2), this sequence (k=3), A353440 (k=4), A353441 (k=5), A353442 (k=6), A353443 (k=7), A353444 (k=8), A333237 (k=9).

%K nonn,base

%O 1,1

%A _Bernard Schott_ and _Robert G. Wilson v_, Apr 22 2022