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

1,2

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A039022 A182402 A079251 * A050051 A252353 A241167

Adjacent sequences: A171782 A171783 A171784 * A171786 A171787 A171788

Keyword

nonn,base

Author

David Scambler, Sep 30 2010

Extensions

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

Status

approved