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
Keywords
Examples
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
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
Programs
-
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 *) -
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
Extensions
Arbitrary limit removed and sequence extended by Phil Carmody, May 26 2011
Comments