A281643 Numbers k such that 7*10^k - 69 is prime.

2, 4, 5, 12, 29, 34, 53, 56, 161, 287, 312, 436, 468, 672, 1316, 1642, 2814, 4171, 6409, 6657, 7914, 9259, 9997, 21253, 29180, 37246, 47936, 48816, 49580, 92414, 97874, 105131, 119006, 137153, 151309, 155450

Offset

1,1

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 9 followed by the digits 31 is prime (see Example section).

a(37) > 3*10^5. - Robert Price, Jul 10 2023

Links

Table of n, a(n) for n=1..36.

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

Makoto Kamada, Search for 69w31.

Example

4 is in this sequence because 7*10^4 - 69 = 69931 is prime.
Initial terms and associated primes:
a(1) = 2, 631;
a(2) = 4, 69931;
a(3) = 5, 699931;
a(4) = 12, 6999999999931;
a(5) = 29, 699999999999999999999999999931; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[7*10^# - 69] &]

Crossrefs

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

Sequence in context: A091071 A353850 A050599 * A102932 A128457 A139485

Adjacent sequences: A281640 A281641 A281642 * A281644 A281645 A281646

Keyword

nonn,more,hard

Author

Robert Price, Jan 25 2017

Extensions

a(32)-a(36) from Robert Price, Jul 03 2019

Status

approved