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 A278996 Numbers of the form (3h+1)*3^(2k)-1 or (3h+2)*3^(2k+1)-1 for h,k in N. 3

%I

%S 0,3,5,6,8,9,12,14,15,18,21,23,24,27,30,32,33,35,36,39,41,42,45,48,50,

%T 51,53,54,57,59,60,62,63,66,68,69,72,75,77,78,80,81,84,86,87,89,90,93,

%U 95,96,99,102,104,105,108,111,113,114,116,117,120,122,123,126,129,131

%N Numbers of the form (3h+1)*3^(2k)-1 or (3h+2)*3^(2k+1)-1 for h,k in N.

%C n is in the sequence if and only if either n == 0, 3, 5, or 6 (mod 9) or n == 8 (mod 9) and (n-8)/9 is in the sequence. - _Robert Israel_, Dec 15 2016

%H Robert Israel, <a href="/A278996/b278996.txt">Table of n, a(n) for n = 1..10000</a>

%H Hao Fu, G.-N. Han, <a href="https://arxiv.org/abs/1601.04370">Computer assisted proof for Apwenian sequences related to Hankel determinants</a>, arXiv preprint arXiv:1601.04370 [math.NT], 2016. See sequence "J" in Section 2.1.

%p filter:= proc(n) local m;

%p (n+1)/3^m mod 3 = 1 + (m mod 2)

%p end proc:

%p select(filter, [\$0..100]); # _Robert Israel_, Dec 15 2016

%t isok[n_]:=Module[{ord=IntegerExponent[n+1,3]},Mod[(n+1)/3^ord,3]==Mod[ord,2]+1];Select[Range[0,131],isok](* _Ray Chandler_, Dec 17 2016 *)

%Y Complement of A278997.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Dec 07 2016

%E More terms from _Robert Israel_, Dec 15 2016

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Last modified July 23 14:44 EDT 2021. Contains 346259 sequences. (Running on oeis4.)