A291868 Numbers k such that (47*10^k - 119)/9 is prime.

2, 3, 9, 15, 39, 45, 59, 137, 180, 224, 264, 476, 491, 504, 1905, 3144, 4784, 10893, 24483, 28602, 82706, 100283, 129789, 131886, 132125

Offset

1,1

Comments

For k>1, numbers such that the digit 5 followed by k-2 occurrences of the digit 2 followed by the digits 09 is prime (see Example section).

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 52w09.

Example

3 is in this sequence because (47*10^3 - 119)/9 = 5209 is prime.
Initial terms and primes associated:
a(1) = 2, 509;
a(2) = 3, 5209;
a(3) = 9, 5222222209;
a(4) = 15, 5222222222222209;
a(5) = 39, 5222222222222222222222222222222222222209; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(47*10^# - 119)/9] &]

Crossrefs

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

Sequence in context: A251239 A124881 A054416 * A092638 A206777 A173809

Adjacent sequences: A291865 A291866 A291867 * A291869 A291870 A291871

Keyword

nonn,more,hard

Author

Robert Price, Sep 04 2017

Extensions

a(22)-a(25) from Robert Price, May 30 2019

Status

approved