A360476 The integers of the sequence appear exactly twice. Between the two copies of k there are k odd integers. The sequence is always extended with the smallest integer not leading to a contradiction.

1, 2, 3, 1, 2, 4, 5, 6, 7, 3, 8, 9, 4, 10, 11, 12, 13, 5, 6, 14, 15, 16, 17, 7, 18, 19, 8, 20, 21, 22, 23, 9, 10, 24, 25, 26, 27, 11, 12, 28, 29, 30, 31, 13, 32, 33, 14, 34, 35, 36, 37, 15, 16, 38, 39, 40, 41, 17, 42, 43, 18, 44, 45, 46, 47, 19, 20, 48, 49, 50

Offset: 1

Author

Eric Angelini, Feb 12 2023

Keywords

• nonn

Examples

			There is one odd integer between the two 1s: this is the integer 3;
there are two odd integers between the two 2s: they are 3 and 1;
there are three odd integers between the two 3s: they are 1, 5 and 7; etc.
		

Crossrefs

Cf. A132291.

Programs

Mathematica

lst={1};k=2;
Do[While[FreeQ[lst,k]&&Count[lst[[First@@Position[lst,t]+1;;]],a_/;OddQ@a]!=t,AppendTo[lst,k];k++];lst=AppendTo[lst,t],{t,25}];lst (* Giorgos Kalogeropoulos, Feb 28 2023 *)

Extensions

More terms from Jinyuan Wang, Feb 14 2023