A294632 Numbers k such that 7*10^k - 99 is prime.

2, 8, 14, 30, 43, 61, 79, 84, 109, 121, 203, 211, 215, 224, 318, 392, 1061, 1304, 1535, 1559, 6989, 9201, 13485, 35462, 39408, 43136, 70680, 126600, 132884, 171535

Offset

1,1

Comments

For k>1, numbers such that the digit 6 followed by k-2 occurrences of the digit 9 followed by the digits 01 is prime (see Example section).

a(31) > 2*10^5.

Links

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

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

Makoto Kamada, Search for 69w01.

Example

2 is in this sequence because 7*10^2 - 99 = 601 is prime.
Initial terms and primes associated:
a(1) = 2, 601;
a(2) = 8, 699999901;
a(3) = 14, 699999999999901;
a(4) = 30, 6999999999999999999999999999901;
a(5) = 43, 69999999999999999999999999999999999999999901; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[7*10^# - 99] &]

Crossrefs

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

Sequence in context: A092346 A196227 A166045 * A073665 A160157 A054598

Adjacent sequences: A294629 A294630 A294631 * A294633 A294634 A294635

Keyword

nonn,more,hard

Author

Robert Price, Nov 05 2017

Extensions

a(28)-a(30) from Robert Price, Jun 29 2019

Status

approved