A045134 Numbers whose base-4 representation contains no 2's and exactly one 3.

3, 7, 12, 13, 19, 23, 28, 29, 48, 49, 52, 53, 67, 71, 76, 77, 83, 87, 92, 93, 112, 113, 116, 117, 192, 193, 196, 197, 208, 209, 212, 213, 259, 263, 268, 269, 275, 279, 284, 285, 304, 305, 308, 309, 323, 327, 332, 333, 339, 343, 348

Offset

1,1

Links

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

Formula

From Robert Israel, Sep 20 2016: (Start)

a(m+(n+1)*2^n) = a(m) + 4^(n+1) for 1 <= m <= (n+1)*2^n.

a(m+(n+1)*2^n) = A000695(m-(n+1)*2^n-1) + 3*4^(n+1) for (n+1)*2^n < m <= (n+2)*2^n. (End)

Maple

N:= 5: # to get all terms < 4^(N+1)
B0:= {0, 1}:
B1:= {3}:
for d from 1 to N do
  B1:= B1 union map(`+`, B0, 3*4^d) union map(`+`, B1, 4^d);
  B0:= B0 union map(`+`, B0, 4^d);
od:
sort(convert(B1, list)); # Robert Israel, Sep 20 2016

Mathematica

Select[Range[400], DigitCount[#, 4, 2]==0&&DigitCount[#, 4, 3]==1&] (* Harvey P. Dale, Dec 25 2012 *)

Crossrefs

Cf. A000695, A007090.

Sequence in context: A056772 A024614 A230109 * A215631 A081695 A290955

Adjacent sequences: A045131 A045132 A045133 * A045135 A045136 A045137

Keyword

nonn,base

Author

Clark Kimberling

Status

approved