A026491 a(n) = least k > a(n-1) such that A001285(k-1) = A001285(n-1) for n >= 1.

1, 4, 5, 8, 10, 12, 13, 16, 17, 20, 21, 24, 26, 28, 29, 32, 34, 36, 37, 40, 42, 44, 45, 48, 49, 52, 53, 56, 58, 60, 61, 64, 65, 68, 69, 72, 74, 76, 77, 80, 81, 84, 85, 88, 90, 92, 93, 96, 98, 100, 101, 104, 106, 108, 109, 112, 113, 116, 117

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001285, A171900.

Programs

Maple

N:= 200: # for terms <= N
S:= StringTools:-ThueMorse(N):
R:= 1: r:= 1:
for n from 1 do
  j:= SearchText(S[n],S,r+1..-1);
  if j = 0 then break fi;
  R:= R, r+j;
  r:= r+j;
  if r >= N then break fi;
od:
R; # Robert Israel, Apr 11 2019
# alternative
A026491 := proc(n)
    option remember ;
    local f,k ;
    if n = 0 then
        1;
    else
        f := A001285(n-1) ;
        for k from procname(n-1)+1 do
            if A001285(k-1) = f then
                return k;
            end if;
        end do:
    end if;
end proc:
seq(A026491(n),n=0..40) ; # R. J. Mathar, Jun 24 2021

Mathematica

a[n_] := a[n] = If[n==0, 1, For[k = a[n-1]+1, True, k++, If[ThueMorse[k-1]==ThueMorse[n-1], Return[k]]]];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Sep 16 2022 *)

Formula

a(n+1)-a(n) = A171900(n+2) for n>=1. - Michel Dekking, Apr 11 2019

Extensions

Clarified NAME with respect to A001285 offsets. - R. J. Mathar, Jun 24 2021