A294125 Numbers k such that (412*10^k - 7)/9 is prime.

1, 16, 22, 26, 29, 55, 83, 110, 128, 176, 187, 566, 1150, 1405, 3515, 7763, 14530, 18398, 26035, 42166, 85897

Offset

1,2

Comments

For k > 1, numbers k such that the digits 45 followed by k occurrences of the digit 7 is prime (see Example section).

a(22) > 2*10^5.

Links

Table of n, a(n) for n=1..21.

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

Makoto Kamada, Search for 457w.

Example

1 is in this sequence because (412*10^1 - 7)/9 = 457 is prime.
Initial terms and associated primes:
a(1) = 1, 457;
a(2) = 16, 457777777777777777;
a(3) = 22, 457777777777777777777777;
a(4) = 26, 4577777777777777777777777777;
a(5) = 29, 4577777777777777777777777777777; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(412*10^# - 7)/9] &]

Crossrefs

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

Sequence in context: A305944 A243972 A091118 * A360735 A341169 A064804

Adjacent sequences: A294122 A294123 A294124 * A294126 A294127 A294128

Keyword

nonn,more,hard

Author

Robert Price, Oct 23 2017

Status

approved