A192817 - OEIS

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

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OFFSET

1,2

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.

LINKS

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

EXAMPLE

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

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 &]

PROG

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