

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
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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



EXAMPLE

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:


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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



