A257037 Numbers k such that 9*R_(k+2) - 7*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

1, 8, 9, 14, 54, 80, 487, 551, 600, 2502, 2544, 5593, 7949, 8635, 13407, 31128, 45504, 45933, 52303, 65121, 167501, 359354, 642225, 1029523, 1170023

Offset

1,2

Comments

Also, numbers k such that 93*10^k - 1 is prime.

Terms up to a(22) from Kamada.

Links

Table of n, a(n) for n=1..25.

Makoto Kamada, Near-repdigit numbers of the form ABAA...AA.

Makoto Kamada, Prime numbers of the form 9299...99.

Predrag Kurtovic, 93*10^642225 - 1, The 5000 Largest Known Primes.

Predrag Kurtovic, 93*10^1029523 - 1, The 5000 Largest Known Primes.

Index entries for primes involving repunits.

Example

For k = 8, 9*R_10 - 7*10^8 = 9999999999 - 700000000 = 9299999999 which is prime, so 8 is a term.

Mathematica

Select[Range[0, 400000], PrimeQ[93*10^#-1 ] &]

Prog

(Magma) [n: n in [0..400] | IsPrime(93*10^n-1)]; // Vincenzo Librandi, Apr 15 2015

Crossrefs

Cf. A002275.

Sequence in context: A373478 A105833 A323249 * A114305 A101765 A306490

Adjacent sequences: A257034 A257035 A257036 * A257038 A257039 A257040

Keyword

more,hard,nonn

Author

Robert Price, Apr 14 2015

Extensions

a(23) from Predrag Kurtovic, Dec 13 2020

a(24) from Predrag Kurtovic, Jan 29 2019

a(25) from Kamada data by Tyler Busby, Apr 14 2024

Status

approved