A045252 - OEIS

%I #23 May 19 2023 19:56:54

%S 9,21,29,39,44,45,47,48,59,71,84,96,101,105,107,108,111,116,129,139,

%T 144,145,147,148,179,189,194,195,197,198,204,214,219,220,222,223,225,

%U 227,228,235,237,238,240,242,243,259,271,279,289

%N Numbers whose base-5 representation contains exactly one 1 and one 4.

%H Robert Israel, <a href="/A045252/b045252.txt">Table of n, a(n) for n = 1..10000</a>

%p d:= 4: # for all terms with up to d base-5 digits.

%p Res:= NULL;

%p for m from 0 to 3^(d-2)-1 do

%p      L:= subs(1=3,convert(3^(d-2)+m,base,3));

%p      for i from 0 to d-2 do

%p        for j from i+1 to d-1 do

%p          xpos:= subs(i=NULL,j=NULL, [$0..d-1]);

%p          x:= add(L[i]*5^xpos[i],i=1..d-2);

%p          Res:= Res, x + 5^i+4*5^j, x+4*5^i+5^j

%p od od od:

%p sort([Res]); # _Robert Israel_, Jan 19 2020

%t Select[Range[300],DigitCount[#,5,1]==DigitCount[#,5,4]==1&] (* _Harvey P. Dale_, May 04 2021 *)

%o (Magma) [k:k in [1..300]| Multiplicity(Intseq(k,5),1) eq 1 and Multiplicity(Intseq(k,5),4) eq 1]; // _Marius A. Burtea_, Jan 20 2020

%Y Cf. A007091.

%K nonn,base

%O 1,1

%A _Clark Kimberling_