A290475 Numbers k such that 4*10^k - 89 is prime.

2, 3, 5, 9, 11, 12, 20, 27, 89, 131, 309, 1065, 3330, 3928, 5724, 12932, 13383, 20760, 20883, 22202, 28860, 32349, 53324, 60572, 64286, 83354, 83740, 101415, 130088, 197268

Offset

1,1

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 11 is prime (see Example section).

a(32) > 2*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 39w11.

Example

3 is in this sequence because 4*10^3 - 89 = 3911 is prime.
Initial terms and associated primes:
a(1) = 2, 311;
a(2) = 3, 3911;
a(3) = 5, 399911;
a(4) = 9; 3999999911;
a(5) = 11, 399999999911; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[4*10^# - 89] &]

Prog

(PARI) lista(nn) = for(n=2, nn, if(ispseudoprime(4*10^n - 89), print1(n, ", "))); \\ Altug Alkan, Aug 03 2017

Crossrefs

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

Sequence in context: A284626 A284847 A186776 * A191183 A078645 A067139

Adjacent sequences: A290472 A290473 A290474 * A290476 A290477 A290478

Keyword

nonn,more,hard,changed

Author

Robert Price, Aug 03 2017

Extensions

a(29)-a(31) from Robert Price, Nov 28 2018

Duplicate a(22) removed by Georg Fischer, Mar 18 2022

Status

approved