

A250041


Numbers n such that m = floor(n/10) is not coprime to n and, if nonzero, m is also a term of the sequence.


9



2, 3, 4, 5, 6, 7, 8, 9, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 42, 44, 46, 48, 50, 55, 60, 62, 63, 64, 66, 68, 69, 70, 77, 80, 82, 84, 86, 88, 90, 93, 96, 99, 200, 202, 204, 205, 206, 208, 220, 222, 224, 226, 228, 240, 242, 243, 244, 246, 248, 249, 260, 262
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OFFSET

1,1


COMMENTS

Equivalent definition 1: Assuming a base b (in this case b=10), let us say that a positive integer k has the property RTNC(b) when m=floor(k/b) is not coprime to k, i.e., gcd(k,m)>1. Then k belongs to this sorted list if (i) it has the property RTNC(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 RTNC(b).
Notes: The acronym RTNC stands for 'RightTruncated is Not Coprime' (negation of the property RTC defined in A250040). We could also say that a(n) are righttruncatable numbers with property RTNC(b).
This particular list is an infinite subset of A248500.


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

243 is a member because (243,24), (24,2) and (2,0) are noncoprime pairs.
155 is not a member because gcd(15,1)=1.


PROG

(PARI) See the link.
(PARI) is_rtnc(n, b=10) = {while (((m=gcd(n\b, n)) != 1), if (m == 0, return (1)); n = n\b; ); return (0); } \\ Michel Marcus, Jan 29 2015


CROSSREFS

Cf. A248500, A250040.
Other lists of righttruncatable numbers with the property RTNC(b): A005823 (b=3), A250037 (b=4), A250039 (b=16), A250043 (b=9), A250045 (b=8), A250047 (b=7), A250049 (b=6), A250051 (b=5).
Sequence in context: A110803 A109795 A248500 * A132029 A281724 A217489
Adjacent sequences: A250038 A250039 A250040 * A250042 A250043 A250044


KEYWORD

nonn,base


AUTHOR

Stanislav Sykora, Dec 07 2014


STATUS

approved



