A303608 - OEIS

%I #30 Jul 21 2021 00:43:55

%S 10,55,91,259,370,385,451,481,505,703,715,1045,1105,1729,2035,2465,

%T 2821,2981,3367,4141,4187,5005,5461,6533,6541,6565,6601,7471,7777,

%U 8149,8401,8695,8905,8911,10001,10585,11111,12403,13366,13981,14245,14645,14701,14911,15211,15841,18685

%N Repunit pseudoprimes: composite numbers k such that (10^k - 1)/9 == 1 (mod k).

%C Composite numbers k such that 10^k == 10 (mod 9k).

%C If k is a term, then so is (10^k - 1)/9. Thus, the sequence is infinite.

%C No terms are divisible by 3. - _Robert Israel_, May 28 2018

%H Robert Israel, <a href="/A303608/b303608.txt">Table of n, a(n) for n = 1..4130</a>

%e (10^10 - 1)/9 = 1111111111 == 1 (mod 10), so the composite 10 is a term.

%e Equivalently, we have the congruence 10^10 == 10 (mod 9*10).

%p filter:=  n -> n mod 3 <> 0 and (10&^n - 10) mod n = 0\ and not isprime(n):

%p select(filter,[$4..10^5]); # _Robert Israel_, May 28 2018

%t Select[Range@ 20000, ! PrimeQ@# && PowerMod[10, #, 9 #] == 10 &] (* _Robert G. Wilson v_, Apr 28 2018 *)

%o (PARI) isok(n) = (n>1) && !isprime(n) && Mod(10, 9*n)^n == 10; \\ _Michel Marcus_, Apr 28 2018

%Y A000864 is a subsequence.

%Y Composite numbers in A067934. - _Michel Marcus_, Apr 27 2018

%K nonn

%O 1,1

%A _Thomas Ordowski_, Apr 27 2018

%E a(4) onward from _Robert G. Wilson v_, Apr 27 2018