A250040 Numbers n such that m = floor(n/10) is coprime to n and, if nonzero, m is also a term of the sequence.

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 101, 103, 107, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 125, 127, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 143, 145, 149, 151, 152, 154, 157, 158, 161, 163, 165, 167, 169, 171, 172, 173, 174, 175

Offset: 1

Author

Stanislav Sykora, Dec 07 2014

Keywords

• nonn
• base

Comments

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.

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

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).

This particular list is an infinite subset of A248499.

Examples

			149, 14, and 1 are members because (149,14), (14,1) and (1,0) are all coprime pairs.
67 is not a member because gcd(67,7)=1, but gcd(6,0)=6.
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..10000
• Stanislav Sykora, PARI/GP scripts for genetic threads, with code and comments.
• Wikipedia, Coprime integers

Crossrefs

Cf. A248499, A250041.

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).

Programs

Maple

F:= proc(a) seq(10*a+d, d = select(t -> igcd(a,t)=1, [$0..9])) end proc:
B[1]:= [1]:
for i from 2 to 4 do
  B[i]:= map(F,B[i-1]);
od:
ListTools:-Flatten([seq(B[i],i=1..4)]); # Robert Israel, Jan 04 2015

PARI

See the link.

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