A294230 Numbers k such that (55*10^k + 377)/9 is prime.

1, 2, 4, 20, 40, 61, 62, 82, 169, 172, 214, 874, 1520, 1652, 2185, 3221, 4012, 4669, 13165, 18922, 91142, 106222

Offset

1,2

Comments

For k > 1, numbers k such that the digit 6 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 61w53.

Example

2 is in this sequence because (55*10^2 + 377)/9 = 653 is prime.
Initial terms and associated primes:
a(1) = 1, 103;
a(2) = 2, 653;
a(3) = 4, 61153;
a(4) = 20, 611111111111111111153;
a(5) = 40, 61111111111111111111111111111111111111153; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(55*10^# + 377)/9] &]

Crossrefs

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

Sequence in context: A108866 A259122 A059206 * A332626 A052004 A353342

Adjacent sequences: A294227 A294228 A294229 * A294231 A294232 A294233

Keyword

nonn,more,hard

Author

Robert Price, Oct 25 2017

Extensions

a(22) from Robert Price, Feb 27 2019

Status

approved