A250745 Start with a(1) = 1; then a(n) = smallest number, not already in the sequence, such that a(n) divides concat(a(1), a(2), ..., a(n)).

1, 2, 3, 5, 10, 4, 8, 6, 11, 20, 13, 7, 9, 12, 15, 18, 14, 25, 30, 24, 16, 32, 40, 29, 50, 100, 26, 52, 39, 21, 28, 35, 42, 17, 34, 51, 23, 46, 27, 36, 45, 43, 19, 38, 68, 48, 60, 75, 90, 54, 56, 58, 22, 44, 33, 55, 97, 125, 200, 64, 80, 69, 66, 88, 70, 41, 82

Offset

1,2

Comments

Like A171785 but without the constraint a(n) > a(n-1).

Among the first 1000 terms, a(n) = n for n = 1, 2, 3, 15, 170, 577, 759, and the numbers not yet found are 149, 298, 347, 401, 447, 454, 457, 467, 487, 509, etc.

Is this sequence a rearrangement of the natural numbers?

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

a(1) = 1;
a(2) = 2 -> 12 /2 = 6;
a(3) = 3 -> 123 / 3 = 41;
Then we cannot use 4 as the next term because 1234 / 4 = 617 / 2.
a(4) = 5 -> 1235 / 5 = 247;
Again, 4, 6, 7, 8 and 9 cannot be used as the next term.
a(5) = 10 -> 123510 / 10 = 12351;
a(6) = 4 -> 1235104 / 4 = 308776;
a(7) = 8 -> 12351048 / 8 = 1543881; etc.

Maple

with(numtheory); P:=proc(q) local a, b, k, n; a:=0; b:={};
for k from 1 to q do for n from 1 to q do if nops({n} intersect b)<1
then if type((a*10^(1+ilog10(n))+n)/n, integer)
then a:=a*10^(1+ilog10(n))+n; b:= b union {n}; print(n); break;
fi; fi; od; od; end: P(10^5);

Crossrefs

Cf. A171785, A240588, A241811, A249398, A249399, A250746, A250747.

Sequence in context: A179332 A081938 A129500 * A109204 A250747 A241262

Adjacent sequences: A250742 A250743 A250744 * A250746 A250747 A250748

Keyword

nonn,base

Author

Paolo P. Lava, Nov 27 2014

Status

approved