A045238 Numbers whose base-5 representation contains exactly one 1 and two 3's.

43, 83, 91, 143, 193, 203, 213, 215, 217, 219, 223, 243, 293, 333, 341, 383, 391, 403, 413, 415, 417, 419, 423, 433, 441, 451, 455, 457, 459, 461, 471, 483, 491, 543, 583, 591, 643, 693, 703, 713, 715, 717, 719, 723, 743, 893

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}:
A13[1]:= {}:
A33[1]:= {}:
A133[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]);
  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]);
  count:= count + nops(A133[n]);
od:
sort([seq(op(A133[i]), i=1..n-1)]); # Robert Israel, Dec 10 2023

Mathematica

Select[Range[900], DigitCount[#, 5, 1]==1&&DigitCount[#, 5, 3]==2&] (* Harvey P. Dale, Dec 16 2017 *)

Crossrefs

Cf. A007091.

Sequence in context: A236839 A183074 A289730 * A139982 A171252 A119487

Adjacent sequences: A045235 A045236 A045237 * A045239 A045240 A045241

Keyword

nonn,base

Author

Clark Kimberling

Status

approved