A283496 Numbers k such that (19*10^k - 37)/9 is prime.

1, 4, 6, 10, 16, 37, 60, 64, 78, 96, 166, 256, 1294, 1398, 2044, 2244, 5080, 7464, 8041, 17929, 18144, 29080, 32623

Offset

1,2

Comments

For k>1, numbers such that the digit 2 followed by k-2 occurrences of the digit 1 followed by the digits 07 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 21w07.

Example

4 is in this sequence because (19*10^4 - 37)/9 = 21107 is prime.
Initial terms and primes associated:
a(1) = 1, 17;
a(2) = 4, 21107;
a(3) = 6, 2111107;
a(4) = 10, 21111111107;
a(5) = 16, 21111111111111107; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(19*10^# - 37)/9] &]

Prog

(PARI) isok(n) = isprime((19*10^n - 37)/9); \\ Indranil Ghosh, Mar 09 2017

Crossrefs

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

Sequence in context: A050887 A078642 A032416 * A117149 A344146 A361564

Adjacent sequences: A283493 A283494 A283495 * A283497 A283498 A283499

Keyword

nonn,more,hard

Author

Robert Price, Mar 08 2017

Status

approved