A248499 Numbers m that are coprime to A059995(m): floor(m/10).

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 31, 32, 34, 35, 37, 38, 41, 43, 45, 47, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 65, 67, 71, 72, 73, 74, 75, 76, 78, 79, 81, 83, 85, 87, 89, 91, 92, 94, 95, 97, 98, 101, 103, 107, 109, 111, 112

Offset: 1

Author

Stanislav Sykora, Oct 07 2014

Keywords

• nonn
• base
• easy

Comments

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.

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

Examples

			1 is a term because gcd(1,0) = 1.
123 is not a term because gcd(123,12) = 3.
165 is a term because 165 and 16 are coprime.
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..20000
• Stanislav Sykora, On some number densities related to coprimes, Stan's Library, Vol. V, Nov 2014, DOI: 10.3247/SL5Math14.005.
• Wikipedia, Coprime integers.

Crossrefs

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

Programs

Mathematica

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

PARI

a=vector(20000);
i=n=0;while(i++,if(gcd(i,i\10)==1,a[n++]=i;if(n==#a,break)));a

Formula

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