A250746 Start with a(0) = 0; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n), a(n-1), ..., a(0)).

0, 1, 2, 3, 5, 10, 15, 18, 19, 35, 42, 51, 55, 70, 85, 93, 95, 106, 155, 217, 310, 745, 1210, 1342, 3355, 5185, 6222, 6330, 9495, 10413, 11115, 12070, 13774, 34435, 41322, 61983, 68870, 1601065116264571, 2217993924228622, 2324778503347862, 2325380783693255

Offset

0,3

Comments

This sequence is infinite. - Robert G. Wilson v, Dec 09 2014

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..46

Example

a(0) = 0;
a(1) = 1 -> 10 / 1 = 10;
a(2) = 2 -> 210 / 2 = 105;
a(3) = 3 -> 3210 / 3 = 1070;
Now we cannot use 4 as the next term because 43210 / 4 = 21605 / 2.
a(4) = 5 -> 32105 / 5 = 6421; etc.

Maple

with(numtheory); P:=proc(q) local a, k, n; print(0); print(1); a:=10;
for n from 2 to q do if type((n*10^(1+ilog10(a))+a)/n, integer)
then a:=n*10^(1+ilog10(a))+a; print(n);
fi; od; end: P(10^9);

Mathematica

f[lst_List] := Block[{k = lst[[-1]] + 1, id = FromDigits@ Flatten@ IntegerDigits@ Reverse@ lst}, While[ Mod[ id, k] > 0, k++]; Append[lst, k]]; Nest[f, {0}, 36] (* or *)
f[lst_List] := Block[{mn = lst[[-1]], id = FromDigits@ Flatten@ IntegerDigits@ Reverse@ lst}, d = Divisors@ id; Append[lst, Min@ Select[d, # > mn &]]]; Nest[f, {0, 1}, 36] (* Robert G. Wilson v, Dec 08 2014 *)

Crossrefs

Cf. A171785, A240588, A241811, A249398, A249399, A250745, A250747.

Sequence in context: A296694 A297253 A014192 * A048315 A093832 A050947

Adjacent sequences: A250743 A250744 A250745 * A250747 A250748 A250749

Keyword

nonn,base

Author

Paolo P. Lava, Nov 27 2014

Extensions

a(37)-a(40) from Robert G. Wilson v, Dec 08 2014

Status

approved