|
%I #19 Mar 19 2020 07:44:46
%S 1,6,9,10,15,18,30,33,45,55,90,91,99,165,246,259,370,385,451,481,495,
%T 505,561,657,703,715,909,1035,1045,1105,1233,1626,1729,2035,2409,2465,
%U 2821,2981,3333,3367,3585,4005,4141,4187,4521,4545,5005,5461,6533,6541
%N Nonprime terms in A121912.
%C 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
%H Amiram Eldar, <a href="/A121014/b121014.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%t Select[Range[10^4], ! PrimeQ[ # ] && PowerMod[10, #, # ] == Mod[10, # ] &] (* _Ray Chandler_, Sep 06 2006 *)
%o (PARI) for(n=1,7000,if(!isprime(n),k=10^n;if((k-10)%n==0,print1(n,",")))) \\ _Klaus Brockhaus_, Sep 06 2006
%Y Cf. A005382, A005939, A121014, A121912.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Sep 06 2006
%E Extended by _Ray Chandler_ and _Klaus Brockhaus_, Sep 06 2006
|
