A045238 - OEIS

%I #18 Dec 10 2023 23:37:46

%S 43,83,91,143,193,203,213,215,217,219,223,243,293,333,341,383,391,403,

%T 413,415,417,419,423,433,441,451,455,457,459,461,471,483,491,543,583,

%U 591,643,693,703,713,715,717,719,723,743,893

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

%H Robert Israel, <a href="/A045238/b045238.txt">Table of n, a(n) for n = 1..10000</a>

%p A0[1]:= {2,4}:

%p A1[1]:= {1}:

%p A3[1]:= {3}:

%p A13[1]:= {}:

%p A33[1]:= {}:

%p A133[1]:= {}:

%p count:= 0:

%p for n from 2 while count < 1000 do

%p   A0[n]:= map(t -> (5*t, 5*t+2, 5*t+4), A0[n-1]);

%p   A1[n]:= map(t -> (5*t,5*t+2,5*t+4), A1[n-1]) union map(t -> 5*t+1, A0[n-1]);

%p   A3[n]:= map(t -> (5*t,5*t+2,5*t+4), A3[n-1]) union map(t -> 5*t+3, A0[n-1]);

%p   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]);

%p   A33[n]:= map(t -> (5*t,5*t+2,5*t+4), A33[n-1]) union map(t -> 5*t+3, A3[n-1]);

%p   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]);

%p   count:= count + nops(A133[n]);

%p od:

%p sort([seq(op(A133[i]),i=1..n-1)]); # _Robert Israel_, Dec 10 2023

%t Select[Range[900],DigitCount[#,5,1]==1&&DigitCount[#,5,3]==2&] (* _Harvey P. Dale_, Dec 16 2017 *)

%Y Cf. A007091.

%K nonn,base

%O 1,1

%A _Clark Kimberling_