A171087 A "run" means a maximal string of numbers that includes exactly one even number; this sequence has the property that the sequence of run lengths is the sequence itself and all natural numbers appear exactly once.

2, 1, 4, 6, 3, 5, 7, 8, 9, 11, 13, 15, 17, 10, 19, 21, 12, 23, 25, 27, 29, 14, 31, 33, 35, 37, 39, 41, 16, 43, 45, 47, 49, 51, 53, 55, 18, 57, 59, 61, 63, 65, 67, 69, 71, 20, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 22, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 24

Offset

1,1

Comments

The rule of construction is: each of the even numbers e(k) = 2*k = 2, 4, 6, 8, 10, ... starts a run of numbers that contains e(k) and a(k)-1 odd numbers not used so far. - R. J. Mathar, Sep 09 2010

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000

Eric Angelini, Runs

E. Angelini, Runs [Cached copy, with permission]

Example

Blocks with run lengths of 2, 1, 4, etc. are (2,1), (4), (6,3,5,7), (8,9,11,13,15,17), (10,19,21), (12,23,25,27,29), ... - R. J. Mathar, Sep 09 2010

Maple

A171087 := proc(n) a := [2, 1] ; modd := 1 ; for p from 2 do rl := op(p, a) ; ev := 2*p ; a := [op(a), ev] ; for o from modd+2 to modd+2*(rl-1) by 2 do a := [op(a), o] ; modd := o ; end do: if nops(a) > n then print(a) ; return; end if; end do: end proc: A171087(100) ; # R. J. Mathar, Sep 09 2010

Crossrefs

Cf. A171083-A171086.

Sequence in context: A262930 A293387 A306015 * A105364 A180405 A171007

Adjacent sequences: A171084 A171085 A171086 * A171088 A171089 A171090

Keyword

nonn

Author

N. J. A. Sloane, Sep 07 2010, based on a posting to the Sequence Fans Mailing List by Eric Angelini, Aug 23 2010

Extensions

More terms from R. J. Mathar and John W. Layman, Sep 09 2010

Status

approved