A178070 Primes dividing repunits R(10^n) for some n.

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 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: 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

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