A102872 List of values of 2^ceiling(log_2(3^k)) - 3^k for k >= 1, sorted in increasing order.

1, 5, 7, 13, 47, 295, 1631, 1909, 6487, 13085, 84997, 502829, 517135, 2428309, 3605639, 5077565, 24062143, 149450423, 808182895, 985222181, 2978678759, 6719515981, 43295774645, 252223018333, 267326277407, 1170495537221, 1738366812781, 1856180682775

Offset

1,2

Comments

a(1)..a(28) verified for k < 2*10^5. For there to be other values that should be inserted into the Data would require log_2(3) to have some extremely good rational approximations, which seems extremely unlikely but hasn't been ruled out completely. - Robert Israel, Jan 04 2017

Links

Table of n, a(n) for n=1..28.

Example

From Robert Israel, Jan 04 2017: (Start)
ceiling(log_2(3^1)) = 2 and 2^2 - 3^1 = 1.
ceiling(log_2(3^2)) = 4 and 2^4 - 3^2 = 7.
ceiling(log_2(3^3)) = 5 and 2^5 - 3^3 = 5.
ceiling(log_2(3^4)) = 7 and 2^7 - 3^4 = 47.
ceiling(log_2(3^5)) = 8 and 2^8 - 3^5 = 13.
These are the first 5 values, so the list starts 1,5,7,13,47. (End)

Maple

Res:= NULL:
for m from 1 to 2*10^5 do
  n:= ilog2(3^m)+1;
  x:= 2^n - 3^m;
  if x <= 10^13 then Res:= Res, x fi;
od:
sort([Res]); # Robert Israel, Jan 04 2017

Mathematica

Delete[Union[Flatten[Table[Table[If [ (2^n > 3^m) && Floor[2^n/3^m] < 2, Abs[2^n - 3^m], 0], {m, 1, n}], {n, 1, 100}], 1]], 1]

Crossrefs

Sequence in context: A174874 A109904 A077781 * A102873 A356847 A342506

Adjacent sequences: A102869 A102870 A102871 * A102873 A102874 A102875

Keyword

nonn

Author

Roger L. Bagula, Mar 01 2005

Extensions

a(27) and a(28), and name changed by Robert Israel, Jan 04 2017

Status

approved