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A102872 List of values of 2^ceiling(log_2(3^k)) - 3^k for k >= 1, sorted in increasing order. 1
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 (list; graph; refs; listen; history; text; internal format)
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)

ceil(ilog_2(3^1) = 2 and 2^2 - 3^1 = 1.

ceil(ilog_2(3^2) = 4 and 2^4 - 3^2 = 7.

ceil(ilog_2(3^3) = 5 and 2^5 - 3^3 = 5.

ceil(ilog_2(3^4) = 7 and 2^7 - 3^4 = 47.

ceil(ilog_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 A342506 A158892

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

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Last modified November 30 22:31 EST 2021. Contains 349426 sequences. (Running on oeis4.)