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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

%I #17 Nov 16 2019 17:04:27

%S 1,5,7,13,47,295,1631,1909,6487,13085,84997,502829,517135,2428309,

%T 3605639,5077565,24062143,149450423,808182895,985222181,2978678759,

%U 6719515981,43295774645,252223018333,267326277407,1170495537221,1738366812781,1856180682775

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

%C 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

%e From _Robert Israel_, Jan 04 2017: (Start)

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

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

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

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

%e ceil(ilog_2(3^5) = 8 and 2^8 - 3^5 = 13.

%e These are the first 5 values, so the list starts 1,5,7,13,47. (End)

%p Res:= NULL:

%p for m from 1 to 2*10^5 do

%p n:= ilog2(3^m)+1;

%p x:= 2^n - 3^m;

%p if x <= 10^13 then Res:= Res, x fi;

%p od:

%p sort([Res]); # _Robert Israel_, Jan 04 2017

%t 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]

%K nonn

%O 1,2

%A _Roger L. Bagula_, Mar 01 2005

%E a(27) and a(28), and name changed by _Robert Israel_, Jan 04 2017

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)