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, 249550

Offset: 1

Author

Robert Price, Jun 17 2015

Keywords

• nonn
• hard
• more

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

Examples

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

Links

• 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.

Crossrefs

Cf. A002275, A069882, A185127.

Programs

Magma

[n: n in [0..500] | IsPrime((4*10^n-7) div 3)]; // Vincenzo Librandi, Jun 18 2015

Mathematica

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

PARI

for(k=1,1500,if(ispseudoprime(4*(10^k-1)/3-1),print1(k,", "))) \\ Hugo Pfoertner, Jul 22 2020

Extensions

a(16) from Kamada data by Tyler Busby, May 03 2024