A093848 (a(n)) is the earliest monotonic sequence starting with a(1)=1 and satisfying a(n)=length of n-th run of consecutive integers with same parity.

1, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 33, 34, 36, 38, 40, 42, 44, 46, 48, 50, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 122, 124

Offset: 1

Author

Benoit Cloitre, May 21 2004

Keywords

• nonn

Comments

There are a(1) odd terms, a(2) even terms, a(3) odd terms, a(4) even terms ... - Benoit Cloitre, May 26 2004

A variation on Golomb's sequence A001462.

Examples

			Sequence begins: (1),(2,4),(5,7,9,11),(12,14,16,18,20),(21,.... since the number of elements in each run of odd or even integers is 1, 2, 4, 5, ... the sequence itself.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A001462, A049039, A169863.

Programs

Maple

A093848 := proc(nmax) local n,par,a,alast,j ; n := 3 ; par := 1 ; a := [1,2,4] ; while nops(a) < nmax do alast := op(-1,a); if type(alast,'even') = type(par,'even') then ; else alast := alast -1 ; end if; for j from 1 to op(n,a) do a := [op(a), alast+2*j] ; end do: par := 1-par ; n := n+1 ; end do: a ; end proc: A093848(120) ; # R. J. Mathar, Jun 22 2010

Mathematica

t={1,2,4}; Do[t=Join[t,Table[t[[-1]]+2*i-1, {i,t[[n]]}]], {n,3,40}]

Formula

it seems that a(n) = 2n - a*n^b + o(n^b) where a and b are 2 suitable constants. b=0.4.... Does b=2-phi where phi is the golden ratio?

Extensions

Terms starting at a(52) corrected by R. J. Mathar, Jun 22 2010