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Lexicographically earliest sequence such that the terms' cumulative sum and the sequence itself have the same digit succession (duplicated terms and zeros allowed).
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%I #15 Feb 25 2020 11:50:00

%S 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,

%T 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,

%U 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

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

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

%H Jean-Marc Falcoz, <a href="/A332804/b332804.txt">Table of n, a(n) for n = 1..20004</a>

%e Below are S, the sequence, and Q, the cumulative sum:

%e S = 10, 1, 1, 1, 2, 1, 3, 1, 5, 1, 6, 1, 9, 2, 0, 2,...

%e Q = 10,11,12,13,15,16,19,20,25,26,32,33,42,44,44,46,...

%e We see that S and Q have the same succession of digits.

%t 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 *)

%Y Cf. A332803.

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 25 2020