A288484 Numbers k such that (298*10^k - 7)/3 is prime.

0, 1, 2, 9, 16, 23, 33, 40, 42, 45, 48, 137, 176, 553, 775, 2072, 3259, 7773, 9457, 17638, 20838, 22277, 32672, 47983, 52308, 54765, 117229, 228177

Offset

1,3

Comments

For k>0, numbers such that the digits 99 followed by k-1 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).

a(29) > 3*10^5.

Links

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

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

Makoto Kamada, Search for 993w1.

Example

2 is in this sequence because (298*10^2 - 7)/3 = 9931 is prime.
Initial terms and primes associated:
a(1) = 0, 97;
a(2) = 1, 991;
a(3) = 2, 9931;
a(4) = 9, 99333333331;
a(5) = 16, 993333333333333331; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(298*10^# - 7)/3] &]

Crossrefs

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

Sequence in context: A136345 A017005 A131189 * A011193 A085960 A051386

Adjacent sequences: A288481 A288482 A288483 * A288485 A288486 A288487

Keyword

nonn,more,hard

Author

Robert Price, Jun 09 2017

Extensions

a(27) from Robert Price, Jun 09 2020

a(28) from Robert Price, Jun 21 2023

Status

approved