A000864 Deceptive nonprimes: composite numbers k that divide the repunit R_{k-1}.

91, 259, 451, 481, 703, 1729, 2821, 2981, 3367, 4141, 4187, 5461, 6533, 6541, 6601, 7471, 7777, 8149, 8401, 8911, 10001, 11111, 12403, 13981, 14701, 14911, 15211, 15841, 19201, 21931, 22321, 24013, 24661, 27613, 29341, 34133

Offset: 1

Author

Tim Ray (c268scm(AT)semovm.semo.edu)

Keywords

• nonn

Comments

Francis and Ray call these numbers "deceptive primes".

Pseudoprimes to base 10, A005939, not divisible by 3. If k is in the sequence, then (10^k-1)/9 is in the sequence, by Steuerwald's theorem; see A005935. - Thomas Ordowski, Apr 10 2016

41041 is the first term that has four prime divisors. - Altug Alkan, Apr 10 2016

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• R. Francis and T. Ray, The deceptive primes to 2.10^7, Missouri J. Math. Sci. 12 (2000), no. 3, 145-158.

Crossrefs

Cf. A002275, A005939.

Programs

Maple

select(t -> not isprime(t) and (10&^(t-1) - 1) mod (9*t) = 0, [seq(t,t=3..10^5,2)]); # Robert Israel, Apr 10 2016

PARI

p=5;forprime(q=7,1e5,forstep(n=p+2,q-2,2,if(n%5 && Mod(10,9*n)^(n-1)==1,print1(n", ")));p=q) \\ Charles R Greathouse IV, Jul 31 2011