A113698 Combinatorial sequence. Begin with 1 then 2 then 12 then 3 then all concatenations of all sizes of 1,2 and 3, then 4, then all concatenations of all sizes of 1,2,3,4 not included earlier etc.

1, 2, 12, 3, 13, 23, 123, 4, 14, 24, 34, 124, 134, 234, 1234, 5, 15, 25, 35, 45, 125, 135, 145, 235, 245, 345, 1235, 1245, 1345, 2345, 12345, 6, 16, 26, 36, 46, 56, 126, 136, 146, 156, 236, 246, 256, 346, 356, 456, 1236, 1246, 1256, 1346, 1356, 1456, 2346, 2356

Offset: 1

Author

Amarnath Murthy, Nov 11 2005

Keywords

• base
• nonn

Comments

The index of n is 2^n for n<10. After 9 if n ( like 13, 23) has appeared earlier it will not appear but it will be used in the concatenation at its turn as mentioned above. needs better description.

The sequence contains groups of integers generated from seeds s=1,2,3,4,... A group is the sorted list of numbers defined by the seed and all concatenations of integers of previous groups with the seed, discarding any duplicates. - R. J. Mathar, Aug 31 2007

Examples

			The group 4, 14, 24, 34, 124, 134, 234, 1234 is generated from the seed s=4 itself and attaching s=4 to the previous elements 1, 2, 12, 3, 13, 23, 123, that is 14, 24, 124, 34, 134, 234, 1234, then sorting within the group (moving 34 between 24 and 124).
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..511

Crossrefs

Cf. A113699.

Programs

Mathematica

Flatten[Table[FromDigits /@ Complement[Subsets[Range[n]], Subsets[Range[n - 1]]], {n, 5}]] (* T. D. Noe, Feb 22 2012 *)

Extensions

More terms from R. J. Mathar, Aug 31 2007