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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 (list; graph; refs; listen; history; text; internal format)
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 * A047842 A047843 A097598

Adjacent sequences:  A250037 A250038 A250039 * A250041 A250042 A250043

KEYWORD

nonn,base

AUTHOR

Stanislav Sykora, Dec 07 2014

STATUS

approved

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Last modified June 27 17:44 EDT 2017. Contains 288790 sequences.