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

1,2

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

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

Example

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

Maple

P:=proc(q) local a, k, n; if q mod 10>0 then a:=q; for k from 1 to ilog10(q) do a:=trunc(a/10^(ilog10(a)+2*(1-k)))*10^(ilog10(q)+2-k)+(q mod 10^(ilog10(q)+1-k)); od;
if type(a/q, integer) then q; fi; fi; end: seq(P(i), i=1..10^5); # Paolo P. Lava, May 23 2017

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

Adjacent sequences: A287333 A287334 A287335 * A287337 A287338 A287339

Keyword

nonn,base

Author

Giovanni Resta, May 23 2017

Status

approved