A287336 Numbers k, not ending in 0, such that inserting a 0 between each pair of adjacent digits results in a multiple of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 15, 18, 45, 111, 126, 222, 285, 333, 444, 555, 666, 777, 888, 999, 1041, 1185, 1395, 1443, 1554, 1665, 1893, 1998, 2082, 2331, 2528, 2757, 2886, 3885, 4662, 4995, 6055, 6993, 7245, 10101, 11111, 11655, 12321, 12987, 13206, 13986

Offset: 1

Author

Giovanni Resta, May 23 2017

Keywords

• nonn
• base

Comments

Sequence is infinite since it contains all the numbers of the form (10^(2*t+1)-1)/9, i.e., repunits with an odd number of digits, like 111, 11111, and so on (A100706).

Examples

			41499585 is a term because 401040909050805 is a multiple of 41499585.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A285176.

Programs

Mathematica

ins[n_, c_] := Block[{d = IntegerDigits[n]}, FromDigits@ Most@ Flatten@ Transpose[{d, c + 0 Range[Length@d]}]]; Select[Range[10^5], Mod[#, 10] > 0 && Mod[ins[#, 0], #] == 0 &]