A288149 Numbers k such that (68*10^k - 257)/9 is prime.

1, 2, 4, 8, 11, 20, 22, 32, 40, 62, 95, 104, 569, 710, 955, 1682, 2933, 4592, 10286, 16634, 19235, 20437, 31024, 48304, 79813, 128645, 148060

Offset

1,2

Comments

For k>1, numbers such that the digit 7 followed by k-2 occurrences of the digit 5 followed by the digits 27 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 75w27.

Example

4 is in this sequence because (68*10^4 - 257)/9 = 75527 is prime.
Initial terms and primes associated:
a(1) = 1, 47;
a(2) = 2, 727;
a(3) = 4, 75527;
a(4) = 8, 755555527;
a(5) = 11, 755555555527; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(68*10^# - 257)/9] &]

Crossrefs

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

Sequence in context: A033956 A282620 A320440 * A159693 A363735 A053437

Adjacent sequences: A288146 A288147 A288148 * A288150 A288151 A288152

Keyword

nonn,more,hard

Author

Robert Price, Jun 05 2017

Extensions

a(26)-a(27) from Robert Price, Jul 27 2019

Status

approved