A252491 a(n) = (10^(n^2) - 1)/(10^n - 1).

1, 101, 1001001, 1000100010001, 100001000010000100001, 1000001000001000001000001000001, 1000000100000010000001000000100000010000001, 100000001000000010000000100000001000000010000000100000001, 1000000001000000001000000001000000001000000001000000001000000001

Offset: 1

Author

M. F. Hasler, Jan 08 2015

Keywords

• nonn
• easy

Comments

When written in base 10, the terms consist of n digits '1' separated by strings of n-1 digits '0'.

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.

a(n) is the product of A019328(d) for all d that divide n^2 but not n. - Robert Israel, Jan 08 2015

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

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

Crossrefs

Cf. A128889 (for 2 instead of 10).

Programs

Maple

seq((10^(n^2)-1)/(10^n-1), n=1..20); # Robert Israel, Jan 08 2015

PARI

A252491(n)=(10^(n^2)-1)\(10^n-1)