A276672 Numbers k such that (19*10^k + 101) / 3 is prime.

1, 3, 4, 9, 10, 12, 13, 16, 20, 37, 57, 66, 106, 116, 127, 355, 396, 547, 2289, 3777, 4500, 7821, 15663, 22746, 25978, 30434, 39682, 119716, 133390, 145093, 200260

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 67 is prime (see Example section).

a(32) > 3*10^5. - Robert Price, Jul 13 2023

Links

Table of n, a(n) for n=1..31.

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

Makoto Kamada, Search for 63w67.

Example

3 is in this sequence because (19*10^3 + 101) / 3 = 6367 is prime.
Initial terms and associated primes:
a(1) = 1, 97;
a(2) = 3, 6367;
a(3) = 4, 63367;
a(4) = 9, 6333333367;
a(5) = 10, 63333333367, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(19*10^# + 101) / 3] &]

Prog

(Magma) [n: n in [0..400] |IsPrime((19*10^n + 101) div 3)]; // Vincenzo Librandi, Sep 13 2016
(PARI) is(n)=ispseudoprime((19*10^n + 101)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A010376 A010388 A283973 * A010400 A010439 A005836

Adjacent sequences: A276669 A276670 A276671 * A276673 A276674 A276675

Keyword

nonn,more

Author

Robert Price, Sep 12 2016

Extensions

a(28)-a(30) from Robert Price, Sep 01 2019

a(31) from Robert Price, Jul 13 2023

Status

approved