A360585 The integers of the sequence appear exactly twice. Between the two copies of k there are k even integers. The sequence is always extended with the smallest integer not leading to a contradiction.

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

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Example

There is one even integer between the two 1s: this is the integer 2;
there are two even integers between the two 2s: they are 4 and 6;
there are three even integers between the two 3s: they are 4, 6 and 2; etc.

Mathematica

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

Crossrefs

Cf. A360476.

Sequence in context: A328395 A283069 A304528 * A175499 A340684 A181440

Adjacent sequences: A360582 A360583 A360584 * A360586 A360587 A360588

Keyword

nonn

Author

Eric Angelini, Feb 12 2023

Extensions

More terms from Jinyuan Wang, Feb 14 2023

Status

approved