A293001 Numbers k such that 69*10^k + 1 is prime.

1, 3, 5, 15, 17, 37, 49, 80, 91, 107, 176, 343, 452, 599, 914, 1393, 1513, 2057, 3332, 6477

Offset

1,2

Comments

For k>0, numbers such that the digits 69 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(21) > 10^5.

Links

Table of n, a(n) for n=1..20.

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

Makoto Kamada, Search for 690w1

Example

3 is in this sequence because 69*10^3 + 1 = 69001 is prime.
Initial terms and primes associated:
a(1) = 1, 691;
a(2) = 3, 69001;
a(3) = 5, 6900001;
a(4) = 15, 69000000000000001;
a(5) = 17, 6900000000000000001; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[69*10^# + 1] &]

Crossrefs

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

Sequence in context: A097856 A071593 A192794 * A018358 A319583 A094358

Adjacent sequences: A292998 A292999 A293000 * A293002 A293003 A293004

Keyword

nonn,more,hard

Author

Robert Price, Sep 27 2017

Status

approved