A045067 Numbers whose base-4 representation contains exactly one 0 and one 3.

12, 19, 28, 35, 44, 49, 50, 52, 56, 71, 75, 77, 78, 83, 92, 99, 108, 113, 114, 116, 120, 135, 139, 141, 142, 147, 156, 163, 172, 177, 178, 180, 184, 197, 198, 201, 202, 209, 210, 212, 216, 225, 226, 228, 232, 279, 283, 285, 286, 295, 299, 301, 302, 309, 310

Offset

1,1

Links

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

Maple

F:= proc(d) local m;
  sort([seq(g(convert(m, base, 2)), m=2^d .. 2^(d+1)-1)])
end proc:
g:= proc(L1) local i, k0, k3, nL, Res, L, Lp, Lpp;
  L:= map(`+`, L1[1..-2], 1);
  nL:= nops(L);
  Res:= NULL;
  for k3 from 0 to nL do
    Lp:= [op(L[1..k3]), 3, op(L[k3+1..nL])];
    for k0 from 0 to nL do
      Lpp:= [op(Lp[1..k0]), 0, op(Lp[k0+1..nL+1])];
      Res:= Res, add(Lpp[i]*4^(i-1), i=1..nL+2);
  od od;
end proc:
seq(op(F(d)), d=0..4); # Robert Israel, Jul 10 2019

Prog

(Python)
from sympy.ntheory import count_digits
def ok(n): c = count_digits(n, 4); return c[0] == c[3] == 1
print([k for k in range(311) if ok(k)]) # Michael S. Branicky, Dec 19 2021

Crossrefs

Cf. A007090.

Subsequence of A039279.

Sequence in context: A349986 A043102 A039279 * A043882 A205718 A117539

Adjacent sequences: A045064 A045065 A045066 * A045068 A045069 A045070

Keyword

nonn,base

Author

Clark Kimberling

Status

approved