login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A252491 a(n) = (10^(n^2) - 1)/(10^n - 1). 4
1, 101, 1001001, 1000100010001, 100001000010000100001, 1000001000001000001000001000001, 1000000100000010000001000000100000010000001, 100000001000000010000000100000001000000010000000100000001, 1000000001000000001000000001000000001000000001000000001000000001 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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
LINKS
MAPLE
seq((10^(n^2)-1)/(10^n-1), n=1..20); # Robert Israel, Jan 08 2015
PROG
(PARI) A252491(n)=(10^(n^2)-1)\(10^n-1)
CROSSREFS
Cf. A128889 (for 2 instead of 10).
Sequence in context: A180053 A138721 A068659 * A015078 A031982 A015041
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Jan 08 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)