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A364664 Lexicographically earliest permutation of the positive integers such that the successive cumulative sums reproduce the sequence itself, digit by digit.

%I A364664 #26 Aug 05 2023 13:01:36
%S A364664 91,10,1,102,20,4,2,24,22,8,230,25,42,7,6,28,45,14,5,3,9,58,15,88,59,
%T A364664 46,226,67,68,16,86,689,69,87,56,77,18,599,189,64,11,90,12,57,13,251,
%U A364664 34,114,27,21,162,185,227,223,282,40,52,423,30,2232,113,275,32,863,37,63,38,83,44,53
%N A364664 Lexicographically earliest permutation of the positive integers such that the successive cumulative sums reproduce the sequence itself, digit by digit.
%H A364664 Giorgos Kalogeropoulos, <a href="/A364664/b364664.txt">Table of n, a(n) for n = 1..5000</a>
%H A364664 Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2023/08/cumulative-sums.html">Cumulative Sums</a>, personal blog.
%e A364664 a(1) = 91
%e A364664 a(1) + a(2) = 101
%e A364664 a(1) + a(2) + a(3) = 102
%e A364664 a(1) + a(2) + a(3) + a(4) = 204
%e A364664 a(1) + a(2) + a(3) + a(4) + a(5) = 224
%e A364664 a(1) + a(2) + a(3) + a(4) + a(5) + a(6) = 228; etc.
%e A364664 The succession of the above results is:
%e A364664   91, 101, 102, 204, 224, 228, ...
%e A364664 The first terms of the sequence are:
%e A364664   91, 10, 1, 102, 20, 4, 2, 24, 22, 8, ...
%e A364664 We see that the successive digits are the same in the two sequences.
%t A364664 Nest[(a=#;AppendTo[a,(new=Flatten[IntegerDigits/@Accumulate@#][[Length@Flatten[IntegerDigits/@a]+1;;]];
%t A364664 k=1;While[MemberQ[a,FromDigits@new[[;;k]]]||new[[k+1]]==0,k++];FromDigits@new[[;;k]])])&,{91,10},77] (* _Giorgos Kalogeropoulos_, Aug 05 2023 *)
%Y A364664 Cf. A309151.
%K A364664 base,nonn
%O A364664 1,1
%A A364664 _Eric Angelini_, Aug 01 2023
%E A364664 More terms from _Giorgos Kalogeropoulos_, Aug 05 2023
%E A364664 a(28) on corrected by _Giorgos Kalogeropoulos_, Aug 05 2023