A294920 Numbers k such that 41*10^k - 1 is prime.

1, 2, 4, 6, 17, 19, 36, 60, 70, 83, 92, 276, 324, 330, 486, 3514, 6062, 10760, 53958, 58920, 101892

Offset

1,2

Comments

For k > 1, numbers such that the digits 40 followed by k occurrences of the digit 9 is prime (see Example section).

a(22) > 2*10^5.

Links

Table of n, a(n) for n=1..21.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 409w.

Example

2 is in this sequence because 41*10^2 - 1 = 409 is prime.
Initial terms and primes associated:
a(1) = 1, 409;
a(2) = 2, 4099;
a(3) = 4, 409999;
a(4) = 6, 40999999;
a(5) = 17, 4099999999999999999; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[41*10^# - 1] &]

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A070325 A199578 A367127 * A046441 A192335 A334390

Adjacent sequences: A294917 A294918 A294919 * A294921 A294922 A294923

Keyword

nonn,more,hard

Author

Robert Price, Nov 10 2017

Extensions

a(21) from Robert Price, Jan 31 2020

Status

approved