A293852 Numbers k such that (37*10^k + 377)/9 is prime.

1, 3, 9, 25, 36, 54, 108, 115, 147, 213, 465, 685, 768, 804, 1951, 3355, 12525, 15097, 15795, 22159, 95895, 185811

Offset

1,2

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 1 followed by the digits 53 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 41w53.

Example

3 is in this sequence because (37*10^3 + 377)/9 = 4153 is prime.
Initial terms and associated primes:
a(1) = 1, 83;
a(2) = 3, 4153;
a(3) = 9, 4111111153;
a(4) = 25, 41111111111111111111111153;
a(5) = 36, 4111111111111111111111111111111111153; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(37*10^# + 377)/9] &]

Crossrefs

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

Sequence in context: A204448 A380050 A032681 * A005209 A112522 A005262

Adjacent sequences: A293849 A293850 A293851 * A293853 A293854 A293855

Keyword

nonn,more,hard

Author

Robert Price, Oct 17 2017

Extensions

a(22) from Robert Price, Nov 02 2018

Status

approved