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Integers m such that the decimal expansion of 1/m contains the digit 2.
7

%I #11 Jul 01 2023 16:54:03

%S 4,5,7,8,13,14,16,17,19,23,28,29,31,32,34,35,36,37,38,39,40,41,42,43,

%T 44,45,46,47,48,49,50,51,52,53,56,57,58,59,61,62,64,67,68,69,70,71,76,

%U 77,78,79,80,81,82,83,85,86,87,89,92,93,94,95,97,98,102,103,105,106,107,108,109

%N Integers m such that the decimal expansion of 1/m contains the digit 2.

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

%e m = 8 is a term since 1/8 = 0.125.

%e m = 44 is a term since 1/44 = 0.022727272727... (here, 2 is the smallest digit).

%e m = 495 is a term since 1/495 = 0.002020202... (here, 2 is the largest digit).

%t f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 125, MemberQ[f@#, 2] &]

%Y A341383 (largest digit=2) and A352156 (smallest digit=2) are subsequences.

%Y Similar with digit k: A352154 (k=0), A353437 (k=1), this sequence (k=2), A353439 (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