A296606 Numbers k such that d*k does not contain the digit d for any d in {1,2,3,4,5,6,7,8,9}.

2, 4, 8, 20, 24, 32, 34, 38, 40, 42, 52, 58, 72, 74, 80, 84, 92, 200, 202, 204, 208, 224, 238, 240, 242, 258, 284, 292, 320, 334, 338, 340, 342, 380, 384, 400, 402, 404, 408, 420, 424, 432, 472, 474, 492, 520, 524, 558, 572, 574, 580, 584, 592, 652, 692, 720

Offset: 1

Author

J. Lowell, Dec 16 2017

Keywords

• base
• nonn

Comments

All terms end in 0, 2, 4, or 8.

A number k ending in 0 is in this sequence if and only if k/10 is in the sequence.

For a number with an odd digit to be in this sequence, the immediately following digit cannot be 0.

For a number with a 6 to be in this sequence, the immediately following digit must be in the 5 to 9 interval.

This sequence has no members with the digit string "67".

Examples

			22*9 = 198, which contains the digit 9 (which is the number by which we multiplied 22) so 22 is not in this sequence.
		

Links

• Iain Fox, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Select[Range[2, 720, 2], Function[n, AllTrue[Range@ 9, FreeQ[IntegerDigits[n #], #] &]]] (* Michael De Vlieger, Dec 16 2017 *)

PARI

is(k) = for(d=1, 9, if(setsearch(Set(digits(d*k)), d), return(0))); 1 \\ Iain Fox, Dec 16 2017

Extensions

More terms from Jon E. Schoenfield, Dec 16 2017