A330674 Lexicographically earliest infinite sequence of distinct nonnegative terms such that a(n+1) is obtained by adding to a(n) the odd digits of a(n) and subtracting the even ones.

1, 2, 0, 3, 6, 4, 5, 10, 11, 13, 17, 25, 28, 18, 7, 14, 8, 9, 12, 15, 21, 20, 16, 19, 29, 36, 33, 39, 51, 57, 69, 72, 77, 91, 101, 103, 107, 115, 122, 119, 130, 134, 22, 23, 24, 26, 27, 32, 30, 31, 35, 43, 42, 34, 37, 47, 50, 55, 65, 64, 54, 38, 40, 41, 44, 45, 46, 48, 49, 52, 53, 61, 56, 58, 59, 73, 83, 78

Offset

1,2

Comments

When an iteration reproduces a term already in the sequence, we cancel this iteration and restart the sequence from there with the smallest integer not yet present in the sequence.

Links

Table of n, a(n) for n=1..78.

Example

As a(1) = 1, we get a(2) = 2 by adding the odd digit 1 to a(1);
as a(2) = 2, we  get a(3) = 0 by subtracting the even digit 2 from a(2);
as a(3) = 0, we stop to iterate (0 would produce 0, already in the sequence) and restart the sequence with a(4) = 3, the smallest integer not present;
as a(4) = 3, we get a(5) = 6 by adding the odd digit 3 to a(4);
as a(5) = 6, we stop to iterate (6-6 produces 0, already in the sequence) and restart the sequence with a(6) = 4, the smallest integer not present;
as a(6) = 4, we stop to iterate (4-4 produces 0, already in the sequence) and restart the sequence with a(7) = 5, the smallest integer not present;
as a(7) = 5, we get a(8) = 10 by adding the odd digit 5 to a(7);
as a(8) = 10, we get a(9) = 11 by adding the odd digit 1 to a(8);
as a(9) = 11, we get a(10) = 13 by adding the odd digits 1 and 1 to a(9); etc.

Mathematica

Nest[Append[#1, If[FreeQ[#1, #2], #2, Block[{k = 3}, While[! FreeQ[#1, k], k++]; k]] & @@ {#1, #1[[-1]] + Total@ Select[#2, OddQ] - Total@ Select[#2, EvenQ]} & @@ {#, IntegerDigits@ #[[-1]]}] &, {1}, 77] (* Michael De Vlieger, Dec 24 2019 *)

Crossrefs

Cf. A036301 (Numbers n such that sum of even digits of n equals sum of odd digits of n).

Sequence in context: A194737 A071089 A144090 * A248966 A021495 A332356

Adjacent sequences: A330671 A330672 A330673 * A330675 A330676 A330677

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Dec 24 2019

Status

approved