A259050 Numbers k such that 3*R_k + 10^k - 2 is prime, where R_k = 11...11 is the repunit (A002275) of length k.

1, 2, 4, 6, 94, 160, 360, 1470, 2898, 3094, 3112, 15698, 17956, 42262, 111032

Offset

1,2

Comments

Also, numbers k such that (4*10^k - 7)/3 is prime.

Terms from Kamada data.

a(16) > 2*10^5.

The corresponding primes are a subset of the palindromes A185127 with a(n)+1 digits [1, 3 repeated a(n)-1 times, 1]: 11, 131, 13331, 1333331, ..., which can be expressed as 2*6-1, 2*66-1, 2*6666-1, 2*666666-1, ... . - Hugo Pfoertner, Jul 22 2020

Links

Table of n, a(n) for n=1..15.

Makoto Kamada, Near-repdigit numbers of the form ABB...BBA.

Makoto Kamada, Prime numbers of the form 133...331.

Index entries for primes involving repunits.

Example

For k=4, 3*R_4 + 10^k - 2 = 3333 + 10000 - 2 = 13331 which is prime.

Mathematica

Select[Range[0, 200000], PrimeQ[(4*10^#-7)/3] &]

Prog

(Magma) [n: n in [0..500] | IsPrime((4*10^n-7) div 3)]; // Vincenzo Librandi, Jun 18 2015
(PARI) for(k=1, 1500, if(ispseudoprime(4*(10^k-1)/3-1), print1(k, ", "))) \\ Hugo Pfoertner, Jul 22 2020

Crossrefs

Cf. A002275, A069882, A185127.

Sequence in context: A098757 A335709 A056012 * A066719 A345269 A345092

Adjacent sequences: A259047 A259048 A259049 * A259051 A259052 A259053

Keyword

nonn,hard,more

Author

Robert Price, Jun 17 2015

Status

approved