A344543 Lexicographically earliest sequence S of distinct positive terms such that the product of the last k digits of S is even, k being the rightmost digit of a(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98

Offset

1,2

Comments

No term ends with zero.

Links

Table of n, a(n) for n=1..80.

Example

a(7) = 7, k = 7, and the product 1*2*3*4*5*6*7 (= 5040) is even;
a(8) = 8, k = 8, and the product 1*2*3*4*5*6*7*8 (= 40320) is even;
a(9) = 9, k = 9, and the product 1*2*3*4*5*6*7*8*9 (= 362880) is even;
a(10) = 12, k = 2, and the product 1*2 (= 2) is even;
a(11) = 13, k = 3, and the product 1*2*3 (= 6) is even;
a(12) = 14, k = 4, and the product 1*2*3*4 (= 24) is even; etc.

Mathematica

a[1]=1; a[n_]:=a[n]=Block[{t=1}, While[(k=t~Mod~10; k>Length[s=Flatten[IntegerDigits/@Join[Array[a, n-1], {t}]]])||k<1||MemberQ[Array[a, n-1], t]||OddQ[Times@@(s[[-k;; ]])], t++]; t]; Array[a, 80] (* Giorgos Kalogeropoulos, May 10 2022 *)

Crossrefs

Cf. A344542.

Sequence in context: A343951 A102234 A174908 * A082757 A239089 A032881

Adjacent sequences: A344540 A344541 A344542 * A344544 A344545 A344546

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, May 30 2021

Status

approved