A344544 Lexicographically earliest sequence S of distinct positive terms such that the sum of the last k digits of S is odd, k being the leftmost digit of a(n).

1, 2, 10, 4, 3, 5, 6, 8, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 30, 40, 31, 21, 22, 32, 41, 23, 24, 33, 25, 26, 34, 42, 35, 27, 28, 36, 43, 29, 50, 51, 37, 38, 80, 39, 52, 60, 81, 44, 45, 46, 47, 48, 49, 70, 53, 71, 54, 82, 100, 61, 72, 55, 73, 56, 83, 57, 62, 58, 90, 59, 63, 64, 84, 65, 66, 67, 74

Offset

1,2

Links

Table of n, a(n) for n=1..79.

Example

a(1) = 1, k = 1, and the sum 1 is odd;
a(2) = 2, k = 2, and the sum 1 + 2 (= 3) is odd;
a(3) = 10, k = 1, and the sum 1 is odd;
a(4) = 4, k = 4, and the sum 2 + 1 + 0 + 4 (= 7) is odd;
a(5) = 3, k = 3, and the sum 0 + 4 + 3 (= 7) is odd;
a(6) = 5, k = 5, and the sum 1 + 0 + 4 + 3 + 5 (= 13) is odd; etc.

Mathematica

a[1]=1; a[n_]:=a[n]=Block[{t=1}, While[(k=First@IntegerDigits@t; k>Length[s=Flatten[IntegerDigits/@Join[Array[a, n-1], {k}]]])||MemberQ[Array[a, n-1], t]||EvenQ@Total[s[[-k;; ]]], t++]; t]; Array[a, 79] (* Giorgos Kalogeropoulos, May 10 2022 *)

Crossrefs

Cf. A344539.

Sequence in context: A234932 A332701 A342158 * A364262 A102512 A344794

Adjacent sequences: A344541 A344542 A344543 * A344545 A344546 A344547

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, May 30 2021

Status

approved