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

1,2

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.

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

Example

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.

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

Prog

(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

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).

Sequence in context: A131835 A262390 A102236 * A321485 A047842 A047843

Adjacent sequences: A250037 A250038 A250039 * A250041 A250042 A250043

Keyword

nonn,base

Author

Stanislav Sykora, Dec 07 2014

Status

approved