A098089
Numbers k such that 7*R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
Original entry on oeis.org
0, 2, 66, 86, 90, 102, 386, 624, 7784, 18536, 113757, 135879
Offset: 1
Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004
If k = 2, we get (7*10^2 + 11)/9 = (700+11)/9 = 79, which is prime.
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[n: n in [0..300] | IsPrime((7*10^n+11) div 9)]; // Vincenzo Librandi, Nov 22 2014
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Do[ If[ PrimeQ[ 7(10^n - 1)/9 + 2], Print[n]], {n, 0, 5000}] (* Robert G. Wilson v, Oct 15 2004 *)
Do[ If[ PrimeQ[((7*10^n) + 11)/9], Print[n]], {n, 0, 8131}] (* Robert G. Wilson v, Sep 27 2004 *)
Select[Range[0, 700], PrimeQ[(7 10^# + 11) / 9] &] (* Vincenzo Librandi, Nov 22 2014 *)
a(1)=0 added and Mathematica programs adapted by
Robert Price, Oct 28 2014
A056693
Numbers k such that 70*R_k + 9 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
Original entry on oeis.org
1, 65, 85, 89, 101, 385, 623, 7783, 18535, 113756, 135878
Offset: 1
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[n: n in [1..400] | IsPrime((7*10^(n+1)+11) div 9)]; Vincenzo Librandi, Nov 22 2014
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Do[ If[ PrimeQ[70*(10^n - 1)/9 + 9], Print[n]], {n, 0, 5000}]
Select[Range[700], PrimeQ[(7 10^(# + 1) + 11) / 9] &] (* Vincenzo Librandi, Nov 22 2014 *)
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
A173808
a(n) = (7*10^n + 11)/9 for n > 0.
Original entry on oeis.org
9, 79, 779, 7779, 77779, 777779, 7777779, 77777779, 777777779, 7777777779, 77777777779, 777777777779, 7777777777779, 77777777777779, 777777777777779, 7777777777777779, 77777777777777779, 777777777777777779, 7777777777777777779, 77777777777777777779, 777777777777777777779
Offset: 1
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[(7*10^n+11)/9: n in [1..20]]; // Vincenzo Librandi Jul 05 2012
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CoefficientList[Series[(9-20*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* Vincenzo Librandi, Jul 05 2012 *)
LinearRecurrence[{11,-10},{9,79},30] (* or *) Table[10*FromDigits[PadRight[{},n,7]]+9,{n,0,30}] (* Harvey P. Dale, Dec 03 2024 *)
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