A295125 Numbers k such that (19*10^k + 521)/9 is prime.

1, 2, 4, 7, 34, 218, 253, 310, 362, 370, 568, 574, 607, 919, 1615, 3968, 5950, 10435, 11887, 176932

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 1 followed by the digits 69 is prime (see Example section).

a(21) > 2*10^5.

Links

Table of n, a(n) for n=1..20.

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

Makoto Kamada, Search for 21w69.

Example

2 is in this sequence because (19*10^2 + 521)/9 = 269 is prime.
Initial terms and associated primes:
a(1) = 1, 79;
a(2) = 2, 269;
a(3) = 4, 21169;
a(4) = 7, 21111169;
a(5) = 34, 21111111111111111111111111111111169; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(19*10^# + 521)/9] &]

Prog

(PARI) isok(k) = isprime((19*10^k + 521)/9); \\ Michel Marcus, Nov 15 2017

Crossrefs

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

Sequence in context: A102124 A280713 A233868 * A082537 A004577 A285940

Adjacent sequences: A295122 A295123 A295124 * A295126 A295127 A295128

Keyword

nonn,more,hard

Author

Robert Price, Nov 15 2017

Extensions

a(20) from Robert Price, May 29 2018

Status

approved