A250041 - OEIS

%I #30 Jan 29 2015 09:18:21

%S 2,3,4,5,6,7,8,9,20,22,24,26,28,30,33,36,39,40,42,44,46,48,50,55,60,

%T 62,63,64,66,68,69,70,77,80,82,84,86,88,90,93,96,99,200,202,204,205,

%U 206,208,220,222,224,226,228,240,242,243,244,246,248,249,260,262

%N Numbers n such that m = floor(n/10) is not coprime to n and, if nonzero, m is also a term of the sequence.

%C Equivalent definition 1: Assuming a base b (in this case b=10), let us say that a positive integer k has the property RTNC(b) when m=floor(k/b) is not coprime to k, i.e., gcd(k,m)>1. Then k belongs to this sorted list if (i) it has the property RTNC(b) and (ii) m is either 0 or belongs also to the list.

%C Equivalent definition 2: Every nonempty prefix of a(n) in base b has the property RTNC(b).

%C Notes: The acronym RTNC stands for 'Right-Truncated is Not Coprime' (negation of the property RTC defined in A250040). We could also say that a(n) are right-truncatable numbers with property RTNC(b).

%C This particular list is an infinite subset of A248500.

%H Stanislav Sykora, <a href="/A250041/b250041.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>

%e 243 is a member because (243,24), (24,2) and (2,0) are noncoprime pairs.

%e 155 is not a member because gcd(15,1)=1.

%o (PARI) See the link.

%o (PARI) is_rtnc(n, b=10) = {while (((m=gcd(n\b, n)) != 1), if (m == 0, return (1)); n = n\b; ); return (0); } \\ _Michel Marcus_, Jan 29 2015

%Y Cf. A248500, A250040.

%Y Other lists of right-truncatable numbers with the property RTNC(b): A005823 (b=3), A250037 (b=4), A250039 (b=16), 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