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

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, 46, 226, 67, 68, 16, 86, 689, 69, 87, 56, 77, 18, 599, 189, 64, 11, 90, 12, 57, 13, 251, 34, 114, 27, 21, 162, 185, 227, 223, 282, 40, 52, 423, 30, 2232, 113, 275, 32, 863, 37, 63, 38, 83, 44, 53

Offset: 1

Author

Eric Angelini, Aug 01 2023

Keywords

• base
• nonn

Examples

			a(1) = 91
a(1) + a(2) = 101
a(1) + a(2) + a(3) = 102
a(1) + a(2) + a(3) + a(4) = 204
a(1) + a(2) + a(3) + a(4) + a(5) = 224
a(1) + a(2) + a(3) + a(4) + a(5) + a(6) = 228; etc.
The succession of the above results is:
  91, 101, 102, 204, 224, 228, ...
The first terms of the sequence are:
  91, 10, 1, 102, 20, 4, 2, 24, 22, 8, ...
We see that the successive digits are the same in the two sequences.
		

Links

• Giorgos Kalogeropoulos, Table of n, a(n) for n = 1..5000
• Eric Angelini, Cumulative Sums, personal blog.

Crossrefs

Cf. A309151.

Programs

Mathematica

Nest[(a=#;AppendTo[a,(new=Flatten[IntegerDigits/@Accumulate@#][[Length@Flatten[IntegerDigits/@a]+1;;]];
k=1;While[MemberQ[a,FromDigits@new[[;;k]]]||new[[k+1]]==0,k++];FromDigits@new[[;;k]])])&,{91,10},77] (* Giorgos Kalogeropoulos, Aug 05 2023 *)

Extensions

More terms from Giorgos Kalogeropoulos, Aug 05 2023

a(28) on corrected by Giorgos Kalogeropoulos, Aug 05 2023