A045243 Numbers whose base-5 representation contains exactly two 1's and three 3's.

843, 1043, 1083, 1091, 2043, 2083, 2091, 2283, 2291, 2331, 3343, 3543, 3583, 3591, 3843, 4093, 4143, 4193, 4203, 4213, 4215, 4217, 4219, 4223, 4243, 4343, 4593, 4793, 4833, 4841, 5043, 5083, 5091, 5143, 5193, 5203, 5213

Offset

1,1

Links

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

Maple

A0[1]:= {2, 4}:
A1[1]:= {1}:
A3[1]:= {3}:
A11[1]:= {}:
A13[1]:= {}:
A33[1]:= {}:
A113[1]:= {}:
A133[1]:= {}:
A333[1]:= {}:
A1133[1]:= {}:
A1333[1]:= {}:
A11333[1]:= {}:
count:= 0:
for n from 2 while count < 1000 do
  A0[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A0[n-1]);
  A1[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A1[n-1]) union map(t -> 5*t+1, A0[n-1]);
  A3[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A3[n-1]) union map(t -> 5*t+3, A0[n-1]);
  A13[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A13[n-1]) union map(t -> 5*t+1, A3[n-1]) union map(t -> 5*t+3, A1[n-1]);
  A33[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A33[n-1]) union map(t -> 5*t+3, A3[n-1]);
  A113[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A113[n-1]) union map(t -> 5*t+1, A13[n-1]) union map(t -> 5*t+3, A11[n-1]);
  A133[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A133[n-1]) union map(t -> 5*t+1, A33[n-1]) union map(t -> 5*t+3, A13[n-1]);
  A333[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A333[n-1]) union map(t -> 5*t+3, A33[n-1]);
  A1133[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A1133[n-1]) union map(t -> 5*t+1, A133[n-1]) union map(t -> 5*t+3, A113[n-1]);
  A1333[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A1333[n-1]) union map(t -> 5*t+1, A333[n-1]) union map(t -> 5*t+3, A133[n-1]);
  A11333[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A11333[n-1]) union map(t -> 5*t+1, A1333[n-1]) union map(t -> 5*t+3, A1133[n-1]);
  count:= count + nops(A11333[n]);
od:
sort([seq(op(A11333[i]), i=1..n-1)]); # Robert Israel, Dec 10 2023

Mathematica

Select[Range[6000], DigitCount[#, 5, 1]==2&&DigitCount[#, 5, 3]==3&] (* Harvey P. Dale, Feb 25 2013 *)

Crossrefs

Cf. A007091.

Sequence in context: A093242 A031527 A252568 * A368778 A096025 A004969

Adjacent sequences: A045240 A045241 A045242 * A045244 A045245 A045246

Keyword

nonn,base

Author

Clark Kimberling

Status

approved