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.

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

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 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 'Right-Truncated is Not Coprime' (negation of the property RTC defined in A250040). We could also say that a(n) are right-truncatable numbers with property RTNC(b).

This particular list is an infinite subset of A248500.

Examples

			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.
		

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. A248500, A250040.

Other lists of right-truncatable 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).

Programs

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