A192817 Numbers that are coprime to their 9's complement.

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 17, 19, 20, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 46, 47, 49, 50, 52, 53, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 79, 80, 82, 83, 85, 86, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104, 106

Offset: 1

Author

Alonso del Arte, Dec 01 2011

Keywords

• nonn
• easy
• base

Comments

If an integer is in this sequence, its 9's complement is in the sequence as well. No multiple of 3 is in this sequence. Multiples of 11 are in the sequence if they have an odd number of digits and they are not also multiples of 3.

Examples

			25 is in the sequence because its 9's complement is 74 and gcd(25, 74) = 1.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061601 (9's complement of n), A201462 (complement).

Programs

Haskell

a192817 n = a192817_list !! (n-1)
a192817_list = [x | x <- [1..], gcd x (a061601 x) == 1]
-- Reinhard Zumkeller, Dec 03 2011

Magma

[n: n in [1..106] | Gcd(10^#Intseq(n)-1,n) eq 1]; // Bruno Berselli, Dec 02 2011

Maple

with(numtheory): P:=proc(q) local k,n; for n from 1 to q do for k from 1 to q do
if type(((n-k)*10^(ilog10(n+k)+1)+n+k)/n,integer) then break; fi; od;
if k=n then print(n); fi; od; end: P(10^4); # Paolo P. Lava, Nov 03 2014

Mathematica

(* First run the program for A061601 to define nineComplement *) Select[Range[100], GCD[#, nineComplement[#]] == 1 &]