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

1,1

Links

Giorgos Kalogeropoulos, Table of n, a(n) for n = 1..5000

Eric Angelini, Cumulative Sums, personal blog.

Example

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.

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 *)

Crossrefs

Cf. A309151.

Sequence in context: A368433 A283896 A284439 * A119656 A368238 A339141

Adjacent sequences: A364661 A364662 A364663 * A364665 A364666 A364667

Keyword

base,nonn

Author

Eric Angelini, Aug 01 2023

Extensions

More terms from Giorgos Kalogeropoulos, Aug 05 2023

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

Status

approved