|
%I #28 Oct 28 2020 03:58:08
%S 1,101,1001001,1000100010001,100001000010000100001,
%T 1000001000001000001000001000001,
%U 1000000100000010000001000000100000010000001,100000001000000010000000100000001000000010000000100000001,1000000001000000001000000001000000001000000001000000001000000001
%N a(n) = (10^(n^2) - 1)/(10^n - 1).
%C When written in base 10, the terms consist of n digits '1' separated by strings of n-1 digits '0'.
%C This sequence is relevant for counterexamples to a conjecture in A086766: If p is prime and a(p) is not prime, then A086766(10^(p-1)) = 0.
%C a(n) is the product of A019328(d) for all d that divide n^2 but not n. - _Robert Israel_, Jan 08 2015
%C If a(n) is a prime then n is a prime. What is the smallest prime term greater than 101 in this sequence? - _Farideh Firoozbakht_, Jan 08 2015
%C According to what precedes, a(n) is prime iff A019328(d) is prime, where d is the only divisor of n^2 which is not a divisor of n, i.e., iff n is a prime and n^2 is in A138940. No such term is known, except for n=2. - _M. F. Hasler_, Jan 09 2015
%p seq((10^(n^2)-1)/(10^n-1), n=1..20); # _Robert Israel_, Jan 08 2015
%o (PARI) A252491(n)=(10^(n^2)-1)\(10^n-1)
%Y Cf. A128889 (for 2 instead of 10).
%K nonn,easy
%O 1,2
%A _M. F. Hasler_, Jan 08 2015
| 