A276845 Numbers k such that (25*10^k - 73) / 3 is prime.

1, 2, 5, 6, 40, 47, 49, 58, 67, 142, 170, 173, 232, 530, 539, 559, 1651, 1858, 2695, 6257, 6714, 8854, 15066, 15091, 16890, 51366, 85249, 135906

Offset

1,2

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 09 is prime (see Example section).

a(29) > 2*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 83w09.

Example

2 is in this sequence because (25*10^2 - 73) / 3 = 809 is prime.
Initial terms and associated primes:
a(1) = 1, 59;
a(2) = 2, 809;
a(3) = 5, 833309;
a(4) = 6, 8333309;
a(5) = 40, 83333333333333333333333333333333333333309, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(25*10^# - 73) / 3] &]

Prog

(PARI) is(n) = ispseudoprime((25*10^n - 73) / 3); \\ Altug Alkan, Sep 20 2016
(Magma) [n: n in [0..500] | IsPrime((25*10^n - 73) div 3)]; // Vincenzo Librandi, Sep 22 2016

Crossrefs

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

Sequence in context: A275285 A360085 A152918 * A365503 A055877 A288799

Adjacent sequences: A276842 A276843 A276844 * A276846 A276847 A276848

Keyword

nonn,more

Author

Robert Price, Sep 20 2016

Extensions

a(28) from Robert Price, Sep 22 2019

Status

approved