A248499 - OEIS

%I #49 Jun 08 2024 00:01:27

%S 1,10,11,12,13,14,15,16,17,18,19,21,23,25,27,29,31,32,34,35,37,38,41,

%T 43,45,47,49,51,52,53,54,56,57,58,59,61,65,67,71,72,73,74,75,76,78,79,

%U 81,83,85,87,89,91,92,94,95,97,98,101,103,107,109,111,112

%N Numbers m that are coprime to A059995(m): floor(m/10).

%C Definition of "being coprime" and special-case conventions are as in Wikipedia. In particular, when m < 10 then floor(m/10) = 0, and zero is coprime only to 1. The complementary sequence is A248500. Note: The first 57 terms a(n) coincide with A069715, but the two sequences are different.

%C The limit mean density of these numbers exists and equals 1223/2100 = A250031(10)/A250033(10). - _Stanislav Sykora_, Dec 08 2014

%H Stanislav Sykora, <a href="/A248499/b248499.txt">Table of n, a(n) for n = 1..20000</a>

%H Stanislav Sykora, <a href="http://dx.doi.org/10.3247/SL5Math14.005">On some number densities related to coprimes</a>, Stan's Library, Vol. V, Nov 2014, DOI: 10.3247/SL5Math14.005.

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

%F { m : gcd(m, floor(m/10)) = 1 }.

%e 1 is a term because gcd(1,0) = 1.

%e 123 is not a term because gcd(123,12) = 3.

%e 165 is a term because 165 and 16 are coprime.

%t Select[ Range@ 120, GCD[#, Floor[#/10]] == 1 &] (* _Robert G. Wilson v_, Oct 22 2014 *)

%o (PARI) a=vector(20000);

%o i=n=0;while(i++,if(gcd(i,i\10)==1,a[n++]=i;if(n==#a,break)));a

%Y Cf. A059995, A248500, A248501, A248502, A250031, A250033.

%K nonn,base,easy

%O 1,2

%A _Stanislav Sykora_, Oct 07 2014