A282505 Numbers k such that (5*10^k - 29)/3 is prime.

1, 2, 3, 4, 5, 6, 12, 32, 63, 116, 154, 221, 267, 468, 605, 749, 1911, 7241, 7406, 7797, 9428, 11094, 43917, 44127, 58384, 131223, 181127

Offset

1,2

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 57 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 16w57.

Example

3 is in this sequence because (5*10^3 - 29)/3 = 1657 is prime.
Initial terms and associated primes:
a(1) = 1, 7;
a(2) = 2, 157;
a(3) = 3, 1657;
a(4) = 4, 16657;
a(5) = 5, 166657; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(5*10^# - 29)/3] &]

Prog

(PARI) isok(k) = isprime((5*10^k - 29)/3); \\ Michel Marcus, Mar 06 2018

Crossrefs

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

Sequence in context: A059460 A125141 A350211 * A165304 A266642 A245450

Adjacent sequences: A282502 A282503 A282504 * A282506 A282507 A282508

Keyword

nonn,more,hard

Author

Robert Price, Feb 16 2017

Extensions

a(26)-a(27) from Robert Price, Mar 05 2018

Status

approved