OFFSET
1,2
COMMENTS
Theorem: If both numbers q and 2q-1 are primes (q is in the sequence A005382) and n=q*(2q-1) then 10^n == 10 (mod n) (n is in the sequence A121014) iff q<5 or mod(q, 20) is in the set {1, 7, 19}. 6,15,91,703,12403,38503,79003,188191,269011,... are such terms. A005939 is a subsequence of this sequence. - Farideh Firoozbakht, Sep 15 2006
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Theorem: If both numbers q and 2q-1 are primes and n=q*(2q-1) then 10^n == 10 (mod n) (n is in the sequence) iff q<5 or mod(q, 20) is in the set {1, 7, 19}. - Farideh Firoozbakht, Sep 11 2006
MATHEMATICA
Select[Range[10^4], ! PrimeQ[ # ] && PowerMod[10, #, # ] == Mod[10, # ] &] (* Ray Chandler, Sep 06 2006 *)
PROG
(PARI) for(n=1, 7000, if(!isprime(n), k=10^n; if((k-10)%n==0, print1(n, ", ")))) \\ Klaus Brockhaus, Sep 06 2006
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 06 2006
EXTENSIONS
Extended by Ray Chandler and Klaus Brockhaus, Sep 06 2006
STATUS
approved