A282458 Numbers k such that (746*10^k + 1)/9 is prime.

0, 1, 3, 4, 12, 16, 27, 39, 190, 192, 327, 378, 444, 958, 1779, 2809, 3396, 3844, 4441, 4452, 9324, 29007, 29464, 99303, 100827, 106618, 107505

Offset

1,3

Comments

For k > 0, numbers k such that the digits 82 followed by k-1 occurrences of the digit 8 followed by the digit 9 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 828w9.

Example

3 is in this sequence because (746*10^3 + 1)/9 = 82889 is prime.
Initial terms and associated primes:
a(1) = 0, 83;
a(2) = 1, 829;
a(3) = 3, 82889;
a(4) = 4, 828889;
a(5) = 12, 82888888888889; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(746*10^# + 1)/9] &]

Crossrefs

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

Sequence in context: A218967 A122757 A280650 * A360755 A348949 A084221

Adjacent sequences: A282455 A282456 A282457 * A282459 A282460 A282461

Keyword

nonn,more,hard

Author

Robert Price, Feb 15 2017

Extensions

a(25)-a(27) from Robert Price, Mar 22 2020

Status

approved