A151754 -id:A151754 - cp's OEIS frontend

A102653 a(n) = 4 * floor(9*2^n/5).

4, 12, 28, 56, 112, 228, 460, 920, 1840, 3684, 7372, 14744, 29488, 58980, 117964, 235928, 471856, 943716, 1887436, 3774872, 7549744, 15099492, 30198988, 60397976, 120795952, 241591908, 483183820, 966367640, 1932735280, 3865470564, 7730941132, 15461882264

Offset: 0

Odimar Fabeny, Feb 02 2005

In binary, each term differs from the previous by a single bit.

Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-2).

Cf. A102650, A102651, A102652.

Table[4Floor[(27 2^n)/15],{n,0,30}] (* or *) LinearRecurrence[ {3,-3,3,-2}, {4,12,28,56},30] (* Harvey P. Dale, Jun 15 2011 *)

a(n)=27<Charles R Greathouse IV, Feb 04 2016

From R. J. Mathar, Feb 20 2011: (Start)
a(n) = 4 * A151754(n+1).
G.f.: 4 * ( 1+x^2-x^3 ) / ( (x-1)*(2*x-1)*(x^2+1) ). (End)
a(0)=4, a(1)=12, a(2)=28, a(3)=56, a(n) = 3*a(n-1)-3*a(n-2)+3*a(n-3)-2*a(n-4). - Harvey P. Dale, Jun 15 2011

Edited by Don Reble, Mar 28 2006

A151752 a(n) is the unique n-digit number with all digits odd that is divisible by 5^n.

Original entry on oeis.org

5, 75, 375, 9375, 59375, 359375, 3359375, 93359375, 193359375, 3193359375, 73193359375, 773193359375, 3773193359375, 73773193359375, 773773193359375, 5773773193359375, 15773773193359375, 515773773193359375, 7515773773193359375, 97515773773193359375

Offset: 1

David W. Wilson, Jun 16 2009

Another way to phrase the proof of uniqueness: after we take the last n-1 digits to be the previous number in the sequence, all odd possibilities for the first digit give different remainders mod 5. By the pigeonhole principle, exactly one of them generates the required number. - Tanya Khovanova, Jun 18 2009

Alois P. Heinz, Table of n, a(n) for n = 1..300
33rd USAMO 2003, Problem 1
Index to sequences related to Olympiads.

Cf. A151753, A151754.

v:=[5];
for i in [2..20] do
    for s in [1, 3, 5, 7, 9] do
         v[i]:=s*10^(i-1)+v[i-1];
           if v[i] mod 5^i eq 0 then
                 break;
           end if;
    end for;
end for;
v; // Marius A. Burtea, Mar 18 2019

a:= proc(n) option remember; local k, l;
      if n=1 then 5
    else l:= a(n-1);
         for k from 1 to 9 by 2
           while (parse(cat(k, l)) mod 5^n)<>0 do od;
         parse(cat(k, l))
      fi
    end:
seq(a(n), n=1..30); # Alois P. Heinz, Jun 18 2009

nxt[n_]:=Module[{x=FromDigits/@(Prepend[IntegerDigits[n],# ]&/@{1,3,5,7,9}),l},l=IntegerLength[n]+1;First[Select[x,Mod[ #,5^l]==0&]]]; NestList[nxt, 5, 25] (* Harvey P. Dale, Jul 06 2009 *)

a(n) = d(n)*10^(n-1) + a(n-1), where d(n), the leading digit of a(n), is one of the odd digits 1, 3, 5, 7, or 9 (forming the complete set of residues modulo 5) and is uniquely defined by the congruence: d(n) == (-a(n-1) / 10^(n-1)) (mod 5). - Max Alekseyev

More terms from Max Alekseyev, Jun 17 2009
Further terms from Alois P. Heinz, Jun 18 2009
More terms from Harvey P. Dale, Jul 06 2009

cp's OEIS Frontend

A102653 a(n) = 4 * floor(9*2^n/5).

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