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

1,2

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

Cf. A005382, A005939, A121014, A121912.

Sequence in context: A037198 A359277 A054020 * A153519 A020219 A175634

Adjacent sequences: A121011 A121012 A121013 * A121015 A121016 A121017

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 06 2006

Extensions

Extended by Ray Chandler and Klaus Brockhaus, Sep 06 2006

Status

approved