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A250037 Numbers n such that m = floor(n/4) is not coprime to n and, if nonzero, m is also a term of the sequence.

%I A250037 #24 Jan 29 2015 09:17:33
%S A250037 2,3,8,10,12,15,32,34,40,42,48,50,51,60,63,128,130,136,138,160,162,
%T A250037 168,170,171,192,194,195,200,202,204,207,240,242,243,252,255,512,514,
%U A250037 520,522,544,546,552,554,555,640,642,648,650,651,672,674,675,680,682
%N A250037 Numbers n such that m = floor(n/4) is not coprime to n and, if nonzero, m is also a term of the sequence.
%C A250037 See the comments in A250041 which all apply, except for the setting of the base, b=4. In particular, they define the property RTNC(b).
%C A250037 If x =12*k+j, 0 <= j <= 11, then x is in the sequence iff either j is in {0,2,3} and 3*k is in the sequence, or j is in {4,6} and 3*k+1 is in the sequence, or j is in {8,10} and 3*k+2 is in the sequence. - _Robert Israel_, Dec 22 2014
%H A250037 Stanislav Sykora, <a href="/A250037/b250037.txt">Table of n, a(n) for n = 1..10000</a>
%H A250037 Stanislav Sykora, <a href="https://oeis.org/wiki/File:GeneticThreads.txt">PARI/GP scripts for genetic threads</a>, with code and comments.
%H A250037 Wikipedia, <a href="http://en.wikipedia.org/wiki/Coprime_integers">Coprime integers</a>
%p A250037 S:= {}:
%p A250037 for n from 1 to 1000 do
%p A250037   m:= floor(n/4);
%p A250037   if igcd(m,n) = 1 then next fi;
%p A250037   if m > 0 and not member(m,S) then next fi;
%p A250037   S:= S union {n}
%p A250037 od:
%p A250037 S; # if using Maple 11 or earlier, uncomment the next line
%p A250037 # sort(convert(S,list)); # _Robert Israel_, Dec 22 2014
%o A250037 (PARI) See the link.
%o A250037 (PARI) is_rtnc(n, b=4) = {while (((m=gcd(n\b, n)) != 1), if (m == 0, return (1)); n = n\b; ); return (0); } \\ _Michel Marcus_, Jan 22 2015
%Y A250037 Cf. A250036, A250041.
%Y A250037 Other lists of right-truncatable numbers with the property RTNC(b):
%Y A250037 A005823 (b=3), A250039 (b=16), A250041 (b=10), A250043 (b=9), A250045 (b=8), A250047 (b=7), A250049 (b=6), A250051 (b=5).
%K A250037 nonn,base
%O A250037 1,1
%A A250037 _Stanislav Sykora_, Dec 07 2014