A295128 Numbers k such that 3*10^k - 37 is prime.

2, 3, 11, 15, 28, 46, 63, 65, 104, 105, 143, 188, 1380, 1599, 3365, 3549, 4535, 9192, 11799, 14745, 45588, 101657

Offset

1,1

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 9 followed by the digits 63 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 29w63.

Example

2 is in this sequence because 3*10^2 - 37 = 263 is prime.
Initial terms and associated primes:
a(1) = 2, 263;
a(2) = 3, 2963;
a(3) = 11, 299999999963;
a(4) = 15, 2999999999999963;
a(5) = 28, 29999999999999999999999999963; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[3*10^# - 37] &]

Prog

(PARI) isok(k) = isprime(3*10^k - 37); \\ Michel Marcus, Nov 15 2017

Crossrefs

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

Sequence in context: A050587 A293026 A178430 * A360520 A066687 A144979

Adjacent sequences: A295125 A295126 A295127 * A295129 A295130 A295131

Keyword

nonn,more,hard,changed

Author

Robert Price, Nov 15 2017

Extensions

a(22) from Robert Price, Jul 07 2018

Status

approved