A344545 Lexicographically earliest sequence S of distinct nonnegative terms such that the sum of the last k digits of S is even, k being the leftmost digit of a(n).

0, 2, 20, 4, 6, 21, 3, 8, 22, 5, 7, 40, 9, 30, 23, 31, 50, 24, 25, 32, 26, 27, 33, 51, 70, 28, 29, 34, 35, 41, 36, 37, 42, 60, 43, 38, 39, 44, 61, 52, 45, 71, 53, 72, 46, 47, 54, 48, 49, 55, 56, 57, 58, 59, 62, 63, 64, 73, 74, 75, 65, 300, 66, 80, 67, 76, 68, 69, 90, 81, 77, 91, 78, 79, 82, 83, 301, 302, 84

Offset

1,2

Links

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

Example

a(1) = 0, k = 0, and the sum 0 is even;
a(2) = 2, k = 2, and the sum 0 + 2 (= 2) is even;
a(3) = 20, k = 2, and the sum 2 + 2 (= 4) is even;
a(4) = 4, k = 4, and the sum 2 + 2 + 0 + 4 (= 8) is even;
a(5) = 6, k = 6, and the sum 0 + 2 + 2 + 0 + 4 + 6 (= 14) is even;
a(6) = 21, k = 2, and the sum 6 + 2  (= 8) is even; etc.

Mathematica

a[1]=0; a[n_]:=a[n]=Block[{k=1}, While[(p=First@IntegerDigits@k; p>Length[s=Flatten[IntegerDigits/@Join[Array[a, n-1], {p}]]])||MemberQ[Array[a, n-1], k]||!EvenQ@Total[s[[-p;; ]]], k++]; k]; Array[a, 79] (* Giorgos Kalogeropoulos, May 09 2022 *)

Crossrefs

Cf. A344540.

Sequence in context: A342077 A077339 A077341 * A076495 A308387 A058403

Adjacent sequences: A344542 A344543 A344544 * A344546 A344547 A344548

Keyword

nonn,base

Author

Eric Angelini and Carole Dubois, May 30 2021

Status

approved