A331117 Lexicographically earliest sequence of distinct terms such that a(n+1) = a(n) + the largest odd digit of a(n), starting with a(n) = 1. If this addition is impossible, or if it leads to a term already in the sequence, restart the sequence from there with the smallest unused integer.

1, 2, 3, 6, 4, 5, 10, 11, 12, 13, 16, 17, 24, 7, 14, 15, 20, 8, 9, 18, 19, 28, 21, 22, 23, 26, 25, 30, 33, 36, 39, 48, 27, 34, 37, 44, 29, 38, 41, 42, 31, 32, 35, 40, 43, 46, 45, 50, 55, 60, 47, 54, 59, 68, 49, 58, 63, 66, 51, 56, 61, 62, 52, 57, 64, 53, 65, 70, 77, 84, 67, 74, 81, 82, 69, 78, 85, 90, 99, 108, 109

Offset

1,2

Comments

This sequence is a permutation of the positive integers.

Links

Carole Dubois, Table of n, a(n) for n = 1..5000

Example

a(1) = 1
a(2) = a(1) + 1 = 2;
as a(2) = 2 has no odd digit, we restart the sequence with a(3) = 3;
a(4) = a(3) + 3 = 6;
as a(4) = 6 has no odd digit, we restart the sequence with a(5) = 4;
as a(5) = 4 has no odd digit, we restart the sequence with a(6) = 5;
a(6) = a(5) + 5 = 10;
a(7) = a(6) + 1 = 11;
a(8) = a(7) + 1 = 12;
a(9) = a(8) + 1 = 13;
a(10) = a(9) + 3 = 16; etc.

Mathematica

Nest[Append[#1, If[FreeQ[#1, #2], #2, Block[{k = 2}, While[! FreeQ[#1, k], k++]; k]] ] & @@ {#1, If[Length@ #2 > 0, #1[[-1]] + #2[[-1]], 1]} & @@ {#, Select[Union@ IntegerDigits[#[[-1]] ], OddQ]} &, {1}, 80] (* Michael De Vlieger, Jan 11 2020 *)

Crossrefs

Sequence in context: A127915 A361966 A358026 * A282841 A254106 A072637

Adjacent sequences: A331114 A331115 A331116 * A331118 A331119 A331120

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jan 10 2020

Status

approved