A293282 Numbers k such that (67*10^k - 7)/3 is prime.

4, 5, 9, 20, 21, 23, 39, 45, 63, 89, 94, 826, 994, 1054, 2886, 4829, 5880, 7928, 17544, 47277, 93226, 127413

Offset

1,1

Comments

For k>1, numbers such that the digits 22 followed by k-2 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 223w1.

Example

5 is in this sequence because (67*10^5 - 7)/3 = 2233331 is prime.
Initial terms and primes associated:
a(1) = 4, 223331;
a(2) = 5, 2233331;
a(3) = 9, 22333333331;
a(4) = 20, 2233333333333333333331;
a(5) = 21, 22333333333333333333331; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(67*10^# - 7)/3] &]

Crossrefs

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

Sequence in context: A153058 A216225 A276645 * A240926 A041032 A041993

Adjacent sequences: A293279 A293280 A293281 * A293283 A293284 A293285

Keyword

nonn,more,hard

Author

Robert Price, Oct 06 2017

Extensions

a(22) from Robert Price, Jan 01 2020

Status

approved