A250040 - OEIS

%I #39 Jan 23 2015 22:41:17

%S 1,10,11,12,13,14,15,16,17,18,19,101,103,107,109,111,112,113,114,115,

%T 116,117,118,119,121,125,127,131,132,133,134,135,136,137,138,139,141,

%U 143,145,149,151,152,154,157,158,161,163,165,167,169,171,172,173,174,175

%N Numbers n such that m = floor(n/10) is 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 RTC(b) when m=floor(k/b) is coprime to k, i.e., gcd(k,m)=1. Then k belongs to this sorted list if (i) it has the property RTC(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 RTC(b).

%C Notes: The acronym RTC stands for 'Right-Truncated is Coprime'. We could also say that a(n) are right-truncatable numbers with property RTC(b).

%C This particular list is an infinite subset of A248499.

%H Stanislav Sykora, <a href="/A250040/b250040.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 149, 14, and 1 are members because (149,14), (14,1) and (1,0) are all coprime pairs.

%e 67 is not a member because gcd(67,7)=1, but gcd(6,0)=6.

%p F:= proc(a) seq(10*a+d, d = select(t -> igcd(a,t)=1, [$0..9])) end proc:

%p B[1]:= [1]:

%p for i from 2 to 4 do

%p   B[i]:= map(F,B[i-1]);

%p od:

%p ListTools:-Flatten([seq(B[i],i=1..4)]); # _Robert Israel_, Jan 04 2015

%o (PARI) See the link.

%o (PARI) is_rtc(n, b=10) = {while (((m=gcd(n\b, n)) == 1), if (m == 0, return (1)); if ((n=n\b) == 0, return (1));); return (0);} \\ _Michel Marcus_, Jan 17 2015

%Y Cf. A248499, A250041.

%Y Other lists of right-truncatable numbers with the property RTC(b): A250036 (b=4), A250038 (b=16), A250042 (b=9), A250044 (b=8), A250046 (b=7), A250048 (b=6), A250050 (b=5).

%K nonn,base

%O 1,2

%A _Stanislav Sykora_, Dec 07 2014