login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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
1,2
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).
LINKS
EXAMPLE
41499585 is a term because 401040909050805 is a multiple of 41499585.
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 &]
CROSSREFS
Cf. A285176.
Sequence in context: A197181 A260352 A049101 * A048406 A081433 A032581
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, May 23 2017
STATUS
approved