A349777 Lexicographically first sequence of positive integers such that all disjoint equivalent sets of K terms have distinct sums for 1 <= K <= 4.

1, 2, 3, 5, 8, 14, 25, 45, 85, 162, 310, 595, 1107, 2052, 3515, 5925, 9798, 16169, 23295, 34303, 53259, 72215, 112624, 153552, 198523, 283570, 370114, 497383, 700022, 840817, 1145415, 1398434, 1717972, 2279969, 2819186, 3436864, 4299205, 5239007, 6335442, 7650495, 9219214

Offset: 1

Author

Santanu Banerjee, Nov 29 2021

Keywords

• nonn

Links

• Gleb Ivanov, Python program.

Crossrefs

Cf. A011185 (k=1..2), A036241 (k=1..3).

A005318 and A276661 are similar sequences.

Programs

Mathematica

a={};k=1;Do[While[(t=1;While[t<=4&&DuplicateFreeQ[Total/@Subsets[Join[a,{k}],{t}]],t++];t)<=4,k++];AppendTo[a,k];Print@k,30] (* Giorgos Kalogeropoulos, Dec 02 2021 *)

Python

# See links.

Extensions

a(13)-a(26) from Alois P. Heinz, Dec 01 2021

a(27)-a(41) from Gleb Ivanov, Dec 02 2021