

A250040


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


9



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
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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 'RightTruncated is Coprime'. We could also say that a(n) are righttruncatable 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[i1]);
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 righttruncatable 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



