A250037 - OEIS

%I #24 Jan 29 2015 09:17:33

%S 2,3,8,10,12,15,32,34,40,42,48,50,51,60,63,128,130,136,138,160,162,

%T 168,170,171,192,194,195,200,202,204,207,240,242,243,252,255,512,514,

%U 520,522,544,546,552,554,555,640,642,648,650,651,672,674,675,680,682

%N 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 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 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 Stanislav Sykora, <a href="/A250037/b250037.txt">Table of n, a(n) for n = 1..10000</a>

%H Stanislav Sykora, <a href="https://oeis.org/wiki/File:GeneticThreads.txt">PARI/GP scripts for genetic threads</a>, with code and comments.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Coprime_integers">Coprime integers</a>

%p S:= {}:

%p for n from 1 to 1000 do

%p   m:= floor(n/4);

%p   if igcd(m,n) = 1 then next fi;

%p   if m > 0 and not member(m,S) then next fi;

%p   S:= S union {n}

%p od:

%p S; # if using Maple 11 or earlier, uncomment the next line

%p # sort(convert(S,list)); # _Robert Israel_, Dec 22 2014

%o (PARI) See the link.

%o (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 Cf. A250036, A250041.

%Y Other lists of right-truncatable numbers with the property RTNC(b):

%Y 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 nonn,base

%O 1,1

%A _Stanislav Sykora_, Dec 07 2014