A290578 Numbers k such that (379*10^k - 1)/9 is prime.

1, 2, 5, 8, 10, 11, 20, 56, 161, 172, 263, 290, 578, 800, 1166, 3382, 3848, 7036, 10487, 12101, 36211, 94337, 138737

Offset

1,2

Comments

For k > 0, numbers k such that the digits 42 followed by k occurrences of the digit 1 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 421w.

Example

2 is in this sequence because (379*10^2 - 1)/9 = 4211 is prime.
Initial terms and associated primes:
a(1) = 1, 421;
a(2) = 2, 4211;
a(3) = 5, 4211111;
a(4) = 8; 4211111111;
a(5) = 10, 421111111111; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(379*10^# - 1)/9] &]

Prog

(PARI) isok(k) = isprime((379*10^k - 1)/9); \\ Michel Marcus, Aug 07 2017

Crossrefs

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

Sequence in context: A352142 A338388 A237525 * A294127 A166955 A286808

Adjacent sequences: A290575 A290576 A290577 * A290579 A290580 A290581

Keyword

nonn,more,hard

Author

Robert Price, Aug 06 2017

Extensions

a(23) from Robert Price, Feb 14 2020

Status

approved