A282138 Numbers k such that (19*10^k - 49)/3 is prime.

1, 2, 3, 4, 5, 6, 7, 21, 22, 101, 111, 132, 174, 201, 265, 335, 388, 537, 1011, 1012, 1254, 6766, 20236, 55833, 104014, 134786, 146181, 159921, 210011

Offset

1,2

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 17 is prime (see Example section).

a(30) > 3*10^5.

Links

Table of n, a(n) for n=1..29.

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

Makoto Kamada, Search for 63w17.

Example

3 is in this sequence because (19*10^3 - 49)/3 = 6317 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 2, 617;
a(3) = 3, 6317;
a(4) = 4, 63317;
a(5) = 5, 633317; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(19*10^# - 49)/3] &]

Crossrefs

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

Sequence in context: A297182 A010354 A070759 * A106275 A303368 A031054

Adjacent sequences: A282135 A282136 A282137 * A282139 A282140 A282141

Keyword

nonn,more,hard

Author

Robert Price, Feb 06 2017

Extensions

a(25)-a(28) from Robert Price, May 18 2019

a(29) from Robert Price, Jun 17 2023

Status

approved