A298981 Numbers m such that there does not exist an integer k < m for which the initial decimal digits of k/m are m.

1, 2, 4, 5, 9, 11, 12, 13, 15, 16, 18, 19, 21, 23, 24, 25, 27, 29, 31, 32, 34, 35, 38, 39, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 61, 65, 68, 75, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 119, 120, 121, 123, 124, 125, 127, 128, 129, 131, 132, 133, 135, 136, 137, 138, 139

Offset: 1

Author

Eric Angelini, M. F. Hasler and Robert G. Wilson v, Jan 30 2018

Keywords

• easy
• nonn
• base

Comments

Inspired by A298232.

Examples

			2 is in the sequence since there is no k such that k/2 would result in a decimal number which begins with 2, i.e., 0.2000. Instead, the decimal number for odd k's begin with 0.5.
		

Crossrefs

Cf. A298232, A051626, A298980, A298982.

Programs

Mathematica

fQ = Compile[{{n, _Integer}}, Block[{k = 1, il = IntegerLength@ n}, While[m = 10^il*k/n; While[ IntegerLength@ Floor@ m < il, m *= 10]; k < n && Floor[m] != n, k++]; k == n]]; Select[Range@140, fQ]

PARI

is_A298981(n)=!A298982(n)

Formula

Complement of A298980.