A364274 Lexicographically earliest sequence of distinct positive terms such that the cumulative sum Q(n) of the first n terms of the sequence has distinct digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 10, 13, 14, 15, 16, 17, 19, 18, 20, 21, 22, 23, 25, 24, 26, 27, 28, 29, 30, 31, 32, 33, 35, 34, 40, 36, 37, 38, 39, 41, 42, 43, 77, 44, 136, 45, 46, 48, 47, 49, 51, 50, 53, 55, 56, 57, 60, 52, 54, 58, 59, 61, 63, 134, 64, 65, 66, 67, 68

Offset

1,2

Comments

The sequence is finite, as Q(n) cannot be > 9876543210. What is the last term of the sequence?

Links

Table of n, a(n) for n=1..70.

Example

a(9) = 9 and Q(9) = 45;
a(10) = 11 and Q(10) = 56: a(10) cannot = 10 as Q(10) would = 55;
a(11) = 12 and Q(11) = 68: a(11) cannot = 10 as Q(11) would = 66;
a(12) = 10 and Q(12) = 78;
a(13) = 13 and Q(13) = 91; etc.

Mathematica

a[1]=1; a[n_]:=a[n]=(k=1; While[!DuplicateFreeQ@IntegerDigits@ Total[Join[c=Array[a, n-1], {k}]]||MemberQ[c, k], k++]; k); Array[a, 70] (* Giorgos Kalogeropoulos, Jul 19 2023 *)

Crossrefs

Cf. A364275.

Sequence in context: A256755 A045876 A033865 * A118764 A226134 A057717

Adjacent sequences: A364271 A364272 A364273 * A364275 A364276 A364277

Keyword

base,nonn

Author

Eric Angelini, Jul 17 2023

Status

approved