A281111 Numbers k such that 97*10^k - 3 is prime.

1, 2, 3, 8, 9, 13, 30, 31, 33, 35, 85, 97, 105, 129, 242, 253, 295, 2810, 2991, 3479, 7902, 16867, 21744, 38687, 51027, 72522, 84033, 91205, 161247, 190295

Offset

1,2

Comments

For k > 0, numbers k such that the digits 96 followed by k-1 occurrences of the digit 9 followed by the digit 7 is prime (see Example section).

a(31) > 3*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 969w7.

Example

3 is in this sequence because 97*10^3 - 3 = 96997 is prime.
Initial terms and associated primes:
a(1) = 1, 967;
a(2) = 2, 9697;
a(3) = 3, 96997;
a(4) = 8, 9699999997;
a(5) = 9, 96999999997; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[97*10^# - 3] &]

Crossrefs

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

Sequence in context: A283160 A281148 A284791 * A301917 A327312 A047243

Adjacent sequences: A281108 A281109 A281110 * A281112 A281113 A281114

Keyword

nonn,more,hard

Author

Robert Price, Jan 14 2017

Extensions

a(29)-a(30) from Robert Price, May 26 2020

Status

approved