A033054 Numbers whose base-3 representation Sum_{i=0..m} d(i)*3^i has d(i)=1 for m-i odd.

1, 2, 4, 7, 12, 13, 14, 21, 22, 23, 37, 40, 43, 64, 67, 70, 111, 112, 113, 120, 121, 122, 129, 130, 131, 192, 193, 194, 201, 202, 203, 210, 211, 212, 334, 337, 340, 361, 364, 367, 388, 391, 394, 577, 580, 583, 604, 607, 610, 631

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Disjoint with A032953 if more than 1 digit.

Programs

Maple

N:= 1000: # to get a(1) to a(N)
K:= ceil((N-4)/3):
Dmax:= ilog[3](ceil(K/2+1)):
A:= Vector(3*K+4):
A[1..4]:= <1,2,4,7>:
for d from 0 to Dmax do
  for k from 2*3^d-1 to min(4*3^d-2,K) do
     A[3*k+2]:= 9*A[k]+3;
     A[3*k+3]:= 9*A[k]+4;
     A[3*k+4]:= 9*A[k]+5
  od:
  for k from 4*3^d-1 to min(2*3^(d+1)-2,K) do
     A[3*k+2]:= 9*A[k]+1;
     A[3*k+3]:= 9*A[k]+4;
     A[3*k+4]:= 9*A[k]+7
  od:
od:
seq(A[i],i=1..N); # Robert Israel, Jun 06 2016

Formula

From Robert Israel, Jun 06 2016: (Start)

a(3n+3) = 9a(n)+4.

If A110654(n) is in A132141 then a(3n+2) = 9a(n)+3 and a(3n+4) = 9a(n)+5

otherwise a(3n+2) = 9a(n)+1 and a(3n+4) = 9a(n)+7.

G.f. satisfies g(x) = 9(x^2+x^3+x^4)g(x^3) + (x+2x^2+4x^3+6x^4-x^5)/(1-x^3) + ((2+2x)/(x+x^2+x^3)) Sum_{k>=1}(x^(2*3^k)-x^(4*3^k)).

(End)

Extensions

Name corrected by Robert Israel, Jun 06 2016