A363446 Increasing sequence such that a(1) = 1 and a(n) is the least integer such that every segment of the sequence a(1),a(2),...,a(n) has a unique sum of elements.

1, 2, 4, 5, 8, 10, 14, 21, 25, 26, 28, 31, 36, 38, 55, 56, 66, 68, 88, 91, 92, 94, 102, 125, 127, 136, 140, 158, 162, 164, 180, 182, 201, 217, 220, 226, 228, 240, 241, 259, 261, 275, 314, 331, 337, 342, 356, 366, 380, 391, 408, 432, 441, 444, 456, 469, 478, 548, 560, 565, 574, 577, 580, 586, 628, 639, 696, 701, 707, 730, 731, 732, 733, 752, 759, 773, 849, 877, 890, 922

Offset: 1

Author

Bartlomiej Pawlik, Jul 09 2023

Keywords

• nonn

Comments

A segment is a subsequence given by consecutive elements.

Examples

			The smallest candidate for a(3) is 3, but the sequence (1,2,3) has two segments with equal sums, namely (1,2) and (3). The next candidate is 4 and every segment of the sequence (1,2,4) has a unique sum, so a(3) = 4.
		

Crossrefs

If we omit the condition that {a(n)} is increasing, we get A101274.

Cf. A276661.