A353438 Integers m such that the decimal expansion of 1/m contains the digit 2.

4, 5, 7, 8, 13, 14, 16, 17, 19, 23, 28, 29, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 61, 62, 64, 67, 68, 69, 70, 71, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 89, 92, 93, 94, 95, 97, 98, 102, 103, 105, 106, 107, 108, 109

Offset: 1

Author

Bernard Schott and Robert G. Wilson v, Apr 22 2022

Keywords

• nonn
• base

Comments

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

Examples

			m = 8 is a term since 1/8 = 0.125.
m = 44 is a term since 1/44 = 0.022727272727... (here, 2 is the smallest digit).
m = 495 is a term since 1/495 = 0.002020202... (here, 2 is the largest digit).
		

Crossrefs

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

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).

Programs

Mathematica

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