A303608 Repunit pseudoprimes: composite numbers k such that (10^k - 1)/9 == 1 (mod k).
10, 55, 91, 259, 370, 385, 451, 481, 505, 703, 715, 1045, 1105, 1729, 2035, 2465, 2821, 2981, 3367, 4141, 4187, 5005, 5461, 6533, 6541, 6565, 6601, 7471, 7777, 8149, 8401, 8695, 8905, 8911, 10001, 10585, 11111, 12403, 13366, 13981, 14245, 14645, 14701, 14911, 15211, 15841, 18685
Offset: 1
Keywords
Examples
(10^10 - 1)/9 = 1111111111 == 1 (mod 10), so the composite 10 is a term. Equivalently, we have the congruence 10^10 == 10 (mod 9*10).
Links
- Robert Israel, Table of n, a(n) for n = 1..4130
Crossrefs
A000864 is a subsequence.
Composite numbers in A067934. - Michel Marcus, Apr 27 2018
Programs
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Maple
filter:= n -> n mod 3 <> 0 and (10&^n - 10) mod n = 0\ and not isprime(n): select(filter,[$4..10^5]); # Robert Israel, May 28 2018
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Mathematica
Select[Range@ 20000, ! PrimeQ@# && PowerMod[10, #, 9 #] == 10 &] (* Robert G. Wilson v, Apr 28 2018 *)
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PARI
isok(n) = (n>1) && !isprime(n) && Mod(10, 9*n)^n == 10; \\ Michel Marcus, Apr 28 2018
Extensions
a(4) onward from Robert G. Wilson v, Apr 27 2018
Comments