A084832 Numbers k such that 2*R_k - 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
4, 18, 100, 121, 244, 546, 631, 1494, 2566, 8088, 262603, 282948, 359860
Offset: 1
Examples
a(1) = 4 because 2*(10^4-1)/9-1 = 2221 is prime. a(2) = 18 means that 222222222222222221 is prime.
Links
Programs
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Maple
select(t -> isprime(2*(10^t-1)/9-1),[$1..1000]); # Robert Israel, Sep 07 2014
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Mathematica
Do[ If[ PrimeQ[2(10^n - 1)/9 - 1], Print[n]], {n, 0, 7000}] (* Robert G. Wilson v, Oct 14 2004; fixed by Derek Orr, Sep 06 2014 *) -
PARI
for(n=1, 10^4, if(ispseudoprime(2*(10^n-1)/9-1), print1(n,", "))) \\ Derek Orr, Sep 06 2014
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Python
from sympy import isprime def afind(limit): n, twoRn = 1, 2 for n in range(1, limit+1): if isprime(twoRn-1): print(n, end=", ") twoRn = 10*twoRn + 2 afind(700) # Michael S. Branicky, Apr 18 2021
Formula
a(n) = A056660(n) + 1.
Extensions
a(8) from Labos Elemer, Jul 15 2004
a(10) from Kamada data by Robert Price, Sep 06 2014
a(11)-a(13) from Kamada data by Tyler Busby, Apr 29 2024
Comments