OFFSET
1,1
COMMENTS
Repunits are the numbers consisting entirely of 1's. The number represented by R(10^n) contains 10^n digits with all 1's. E.g., R(10^1) = 1111111111.
A prime p > 5 is here if the multiplicative order of 10 (mod p) is of the form 2^i*5^j, with i and j nonnegative.
Includes all terms > 5 of A077497. - Robert Israel, Nov 05 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..110
Dario Alejandro Alpern, Known prime factors of Googolplexplex - 1
Project Euler, Problem 133: Repunit nonfactors
Robert P. Munafo, Notable Properties of Specific Numbers
EXAMPLE
17 divides R(10^4), so is in the sequence. - Phil Carmody, May 26 2011
Note that R(10^n) == 1 mod 3 for all n, so 3 is not a member. - N. J. A. Sloane, Jun 18 2014
MAPLE
filter:= proc(p) local v;
if not isprime(p) then return false fi;
v:= numtheory:-order(10, p);
v = 2^padic:-ordp(v, 2) * 5^padic:-ordp(v, 5)
end proc:
select(filter, [seq(i, i=7 .. 10^6, 2)]); # Robert Israel, Nov 05 2024
MATHEMATICA
Select[Prime[Range[4, 100000]], Complement[First /@ FactorInteger[MultiplicativeOrder[10, #]], {2, 5}] == {} &] (* T. D. Noe, May 26 2011 *)
PROG
(PARI) g=10^30; forprime(p=7, 1000000, z=znorder(Mod(10, p)); if(gcd(z, g)==z, print1(p", "))) \\ Phil Carmody, May 26 2011
(PARI) upTo(lim)=my(v=List(), g=10^(log(lim)\log(2))); forprime(p=7, lim, if(g%znorder(Mod(10, p))==0, listput(v, p))); Vec(v) \\ Charles R Greathouse IV, May 26 2011
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Shashank Sharma, May 19 2010, Aug 04 2010
EXTENSIONS
Arbitrary limit removed and sequence extended by Phil Carmody, May 26 2011
STATUS
approved