A078649 Numbers n such that A000002(n)=A000002(n+1) where A000002 is the Kolakoski sequence.

2, 4, 8, 11, 13, 16, 18, 22, 26, 28, 31, 35, 38, 40, 44, 48, 51, 53, 56, 58, 62, 65, 67, 70, 74, 78, 80, 83, 85, 89, 92, 94, 97, 99, 103, 107, 110, 112, 115, 119, 121, 124, 126, 130, 133, 135, 138, 140, 144, 148, 150, 153, 157, 160, 162, 165, 167, 171, 175, 178, 180

Offset: 1

Author

Benoit Cloitre, Dec 14 2002

Keywords

• nonn
• easy

Comments

Complement sequence of A054353. - Benoit Cloitre, Feb 07 2009

This sequence is the union of A074262 and A074263. - Nathaniel Johnston, May 02 2011

A054354(a(n)-1) = 0. - Reinhard Zumkeller, Aug 03 2013

This is a subsequence of A216345. In particular, this consists of A216345(i) such that A000002(i) = A216345(i+1)-A216345(i) = 2. A013948 is the sequence of all such i. - Danny Rorabaugh, Mar 13 2015

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054353, A074262, A074263, A013948, A216345.

Programs

Haskell

a078649 n = a078649_list !! (n-1)
a078649_list = map (+ 1) $ filter ((== 0) . a054354) [1..]
-- Reinhard Zumkeller, Aug 03 2013

Maple

isA078649 := proc(n)
    if A000002(n) = A000002(n+1) then
        true;
    else
        false;
    end if;
end proc:
A078649 := proc(n)
    option remember;
    if n = 1 then
        2;
    else
        for a from procname(n-1)+1 do
            if isA078649(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A078649(n),n=1..50) ; # R. J. Mathar, Nov 15 2014

Mathematica

a2 = {1, 2, 2}; Do[ a2 = Join[a2, {1+Mod[n-1, 2]}], {n, 3, 80}, {a2[[n]]}]; a3 = Accumulate[a2]; Complement[ Range[ Last[a3]], a3] (* Jean-François Alcover, Jun 18 2013 *)

Formula

a(n) is probably asymptotic to 3*n.

a(n) = A216345(A013948(n)). - Danny Rorabaugh, Mar 13 2015