A332804 Lexicographically earliest sequence such that the terms' cumulative sum and the sequence itself have the same digit succession (duplicated terms and zeros allowed).

10, 1, 1, 1, 2, 1, 3, 1, 5, 1, 6, 1, 9, 2, 0, 2, 5, 2, 6, 3, 2, 3, 3, 4, 2, 4, 4, 4, 4, 4, 6, 5, 1, 5, 3, 5, 9, 6, 2, 6, 4, 6, 7, 7, 0, 7, 4, 7, 6, 8, 0, 8, 4, 8, 8, 9, 2, 9, 6, 1, 0, 2, 1, 0, 7, 1, 0, 8, 1, 1, 3, 1, 1, 6, 1, 2, 1, 1, 3, 0, 1, 3, 6, 1, 3, 8, 1, 4, 4, 1, 4, 8, 1, 5, 4, 1, 6, 1, 1, 6, 8, 1, 6, 8

Offset

1,1

Comments

The variant where duplicated terms and zero are forbidden is A332803.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..20004

Example

Below are S, the sequence, and Q, the cumulative sum:
S = 10, 1, 1, 1, 2, 1, 3, 1, 5, 1, 6, 1, 9, 2, 0, 2,...
Q = 10,11,12,13,15,16,19,20,25,26,32,33,42,44,44,46,...
We see that S and Q have the same succession of digits.

Mathematica

s={10, 1}; q={1, 0, 1, 1}; t=11; p=4; While[ Length[s] < 105, v = q[[p++]]; AppendTo[s, v]; t += v; q = Join[q, IntegerDigits@ t]]; s (* Giovanni Resta, Feb 25 2020 *)

Crossrefs

Cf. A332803.

Sequence in context: A360159 A284100 A279051 * A010178 A070596 A306363

Adjacent sequences: A332801 A332802 A332803 * A332805 A332806 A332807

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Feb 25 2020

Status

approved