

A178070


Primes dividing repunits R(10^n) for some n.


3



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
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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 is here if the multiplicative order of 10 (mod p) is of the form 2^i*5^j, with i and j nonnegative.


LINKS

Table of n, a(n) for n=1..51.
Dario Alejandro Alpern, Known prime factors of Googolplexplex  1
Project Euler, Problem 133
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


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

Cf. A227246.
Sequence in context: A057473 A267291 A073649 * A243222 A090609 A187057
Adjacent sequences: A178067 A178068 A178069 * A178071 A178072 A178073


KEYWORD

nonn


AUTHOR

Shashank Sharma, May 19 2010, Aug 04 2010


EXTENSIONS

Arbitrary limit removed and sequence extended by Phil Carmody, May 26 2011


STATUS

approved



