A341869 For any k, the cumulative sum of the terms a(1) + a(2) + a(3) + ... + a(k) and the cumulative sum of their digits so far are odd. This is the lexicographically earliest sequence of distinct terms > 0 with this property.

1, 2, 4, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 110, 112, 114, 116, 118, 130, 132, 134, 136, 138, 150, 152, 154, 156, 158, 170, 172, 174, 176, 178, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 220, 222, 224, 226, 228, 240, 242, 244, 246, 248

Offset

1,2

Comments

This is A179082 (even numbers having an even sum of digits in their decimal representation) where the first term [0] is replaced by [1].

Links

Table of n, a(n) for n=1..65.

Example

Sequence                 = 1,2,4, 6, 8,20,22,24, 26, 28, 40, 42, 44 ...
Cumulative sum of terms  = 1 3 7 13 21 41 63 87 113 141 181 223 267 ...
Cumulative sum of digits = 1 3 7 13 21 23 27 33  41  51  55  61  69 ...

Mathematica

a[1]=1; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[q=Array[a, n-1], k]||EvenQ@Total[s=Join[q, {k}]]||EvenQ@Total[Flatten[IntegerDigits/@s]], k++]; k]; Array[a, 65] (* Giorgos Kalogeropoulos, May 11 2022 *)

Crossrefs

Cf. A179082.

Sequence in context: A273892 A352546 A179082 * A194376 A062897 A014263

Adjacent sequences: A341866 A341867 A341868 * A341870 A341871 A341872

Keyword

base,nonn

Author

Eric Angelini, Feb 22 2021

Status

approved