A290033 Numbers k such that 2*10^k - 69 is prime.

2, 3, 5, 8, 30, 50, 52, 120, 160, 215, 260, 306, 537, 539, 10690, 13888, 15495, 16874, 18448, 22233, 59394, 103749

Offset

1,1

Comments

For k>1, numbers such that the digit 1 followed by k-2 occurrences of the digit 9 followed by the digits 31 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 19w31.

Example

3 is in this sequence because 2*10^3 - 69 = 1931 is prime.
Initial terms and primes associated:
a(1) = 2, 131;
a(2) = 3, 1931;
a(3) = 5, 199931;
a(4) = 8, 199999931;
a(5) = 30, 1999999999999999999999999999931; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[2*10^# - 69] &]

Crossrefs

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

Sequence in context: A318763 A041731 A041331 * A004091 A072210 A273003

Adjacent sequences: A290030 A290031 A290032 * A290034 A290035 A290036

Keyword

nonn,more,hard

Author

Robert Price, Jul 18 2017

Extensions

a(22) from Robert Price, Mar 22 2018

Status

approved