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A178070
Primes dividing repunits R(10^n) for some n.
4
11, 17, 41, 73, 101, 137, 251, 257, 271, 353, 401, 449, 641, 751, 1201, 1409, 1601, 3541, 4001, 4801, 5051, 9091, 10753, 15361, 16001, 19841, 21001, 21401, 24001, 25601, 27961, 37501, 40961, 43201, 60101, 62501, 65537, 69857, 76001, 76801, 160001, 162251, 163841, 307201, 453377, 524801, 544001, 670001, 952001, 976193, 980801
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
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
Sequence in context: A057473 A267291 A073649 * A243222 A090609 A187057
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