A282571 Numbers k such that 2*10^k - 27 is prime.

2, 3, 4, 9, 26, 40, 41, 56, 82, 114, 150, 155, 203, 213, 578, 2638, 4761, 10202, 14211, 16421, 18047, 30701, 53834, 66826, 115784, 141407

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 9 followed by the digits 73 is prime (see Example section).

a(27) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 19w73.

Example

3 is in this sequence because 2*10^3 - 27 = 1973 is prime.
Initial terms and associated primes:
a(1) = 2, 173;
a(2) = 3, 1973;
a(3) = 4, 19973;
a(4) = 9, 1999999973;
a(5) = 26, 199999999999999999999999973; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[2*10^# - 27] &]

Prog

(PARI) isok(k) = isprime(2*10^k - 27); \\ Michel Marcus, Feb 19 2017

Crossrefs

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

Sequence in context: A085612 A073915 A076381 * A063455 A001144 A121253

Adjacent sequences: A282568 A282569 A282570 * A282572 A282573 A282574

Keyword

nonn,more,hard

Author

Robert Price, Feb 18 2017

Extensions

a(25)-a(26) from Robert Price, May 05 2018

Status

approved