A171785 Start with a(1) = 1; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(1), a(2), ..., a(n)).

1, 2, 3, 5, 10, 12, 15, 20, 25, 30, 39, 44, 50, 100, 101, 125, 150, 188, 200, 220, 230, 250, 272, 304, 320, 370, 376, 400, 500, 525, 600, 615, 625, 1000, 1250, 1487, 1500, 1590, 1696, 1750, 2000, 2245, 2500, 3000, 3090, 3125, 3800, 4000, 5000, 5725, 6122, 7025

Offset: 1

Author

David Scambler, Sep 30 2010

Keywords

• nonn
• base

Comments

Primes appearing so far are 2, 3, 5, 101, 1487.

Examples

			1: 1 divides 1
1,2: 2 divides 12
1,2,3: 3 divides 123
1,2,3,4: 4 does NOT divide 1234, so
1,2,3,5: 5 divides 1235
etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..584

Crossrefs

See A029455 for numbers that divide the concatenation of all numbers <= n.

Programs

Mathematica

f[s_List] := Block[{k = s[[ -1]] + 1, conc = FromDigits[Flatten@ IntegerDigits@s]}, While[ Mod[conc*10^Floor[ Log[10, k] + 1] + k, k] != 0, k++ ]; Append[s, k]]; Nest[f, {1}, 51] (* Robert G. Wilson v, Oct 14 2010 *)
nxt[{a_,c_}]:=Module[{k=a+1},While[!Divisible[c*10^IntegerLength[k]+ k, k], k++];{k,c*10^IntegerLength[k]+k}]; Transpose[NestList[nxt,{1,1},60]][[1]] (* Harvey P. Dale, Mar 08 2015 *)

Extensions

More terms from Robert G. Wilson v, Oct 14 2010