A278997 - OEIS

%I #30 Nov 06 2021 23:17:26

%S 1,2,4,7,10,11,13,16,17,19,20,22,25,26,28,29,31,34,37,38,40,43,44,46,

%T 47,49,52,55,56,58,61,64,65,67,70,71,73,74,76,79,82,83,85,88,91,92,94,

%U 97,98,100,101,103,106,107,109,110,112,115,118,119,121,124,125,127,128,130

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

%C n is in the sequence if and only if either n == 1, 2, 4, or 7 (mod 9) or n == 8 (mod 9) and (n-8)/9 is in the sequence. - _Robert Israel_, Dec 18 2016

%H Ray Chandler, <a href="/A278997/b278997.txt">Table of n, a(n) for n = 1..10000</a>

%H Hao Fu and 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 "K" in Section 2.1.

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

%p   m:= padic:-ordp(n+1,3);

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

%p end proc:

%p select(filter, [$0..100]); # _Robert Israel_, Dec 18 2016

%t isok[n_]:=Module[{ord=IntegerExponent[n+1,3]},Mod[(n+1)/3^ord,3]!=Mod[ord,2]+1];Select[Range[0,100],isok](* _Ray Chandler_, Dec 17 2016 *)

%Y Complement of A278996.

%Y Positions of 1's in A156595.

%K nonn

%O 1,2

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

%E More terms from _Ray Chandler_, Dec 17 2016