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

1,2

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.

Links

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

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?

Example

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.

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}]

Crossrefs

Cf. A001462, A049039, A169863.

Sequence in context: A184858 A083026 A047379 * A049039 A325101 A301728

Adjacent sequences: A093845 A093846 A093847 * A093849 A093850 A093851

Keyword

nonn

Author

Benoit Cloitre, May 21 2004

Extensions

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

Status

approved