A121014 Nonprime terms in A121912.

1, 6, 9, 10, 15, 18, 30, 33, 45, 55, 90, 91, 99, 165, 246, 259, 370, 385, 451, 481, 495, 505, 561, 657, 703, 715, 909, 1035, 1045, 1105, 1233, 1626, 1729, 2035, 2409, 2465, 2821, 2981, 3333, 3367, 3585, 4005, 4141, 4187, 4521, 4545, 5005, 5461, 6533, 6541

Offset: 1

Author

N. J. A. Sloane, Sep 06 2006

Keywords

• nonn
• easy

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

Crossrefs

Cf. A005382, A005939, A121014, A121912.

Programs

Mathematica

Select[Range[10^4], ! PrimeQ[ # ] && PowerMod[10, #, # ] == Mod[10, # ] &] (* Ray Chandler, Sep 06 2006 *)

PARI

for(n=1,7000,if(!isprime(n),k=10^n;if((k-10)%n==0,print1(n,",")))) \\ Klaus Brockhaus, Sep 06 2006

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

Extensions

Extended by Ray Chandler and Klaus Brockhaus, Sep 06 2006