A294634 Numbers k such that (754*10^k - 7)/9 is prime.

0, 2, 3, 5, 6, 9, 30, 38, 66, 110, 135, 168, 470, 477, 654, 1635, 1875, 2823, 12162, 23984, 32859, 33609, 34814, 39162, 58748, 82250, 161816

Offset

1,2

Comments

Numbers k such that the digits 83 followed by k occurrences of the digit 7 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 837w.

Example

2 is in this sequence because (754*10^2 - 7)/9 = 8377 is prime.
Initial terms and associated primes:
a(1) = 0, 83;
a(2) = 2, 8377;
a(3) = 3, 83777;
a(4) = 4, 8377777;
a(5) = 6, 83777777777; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(754*10^# - 7)/9] &]

Crossrefs

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

Sequence in context: A272776 A055690 A108861 * A051896 A061939 A029503

Adjacent sequences: A294631 A294632 A294633 * A294635 A294636 A294637

Keyword

nonn,more,hard

Author

Robert Price, Nov 05 2017

Extensions

a(27) from Robert Price, May 02 2020

Status

approved