A281642 Numbers k such that 4*10^k - 57 is prime.

3, 7, 10, 15, 28, 35, 70, 183, 243, 298, 366, 388, 607, 791, 827, 1704, 1732, 1743, 2755, 2766, 2983, 3312, 7173, 16365, 18234, 102163, 104461, 136813, 154078

Offset

1,1

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 43 is prime (see Example section).

a(30) > 2*10^5.

Links

Table of n, a(n) for n=1..29.

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

Makoto Kamada, Search for 39w43.

Example

3 is in this sequence because 4*10^3 - 57 = 3943 is prime.
Initial terms and associated primes:
a(1) = 3, 3943;
a(2) = 7, 39999943;
a(3) = 10, 39999999943;
a(4) = 15, 3999999999999943;
a(5) = 28, 39999999999999999999999999943; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[4*10^# - 57] &]

Crossrefs

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

Sequence in context: A307612 A330160 A373186 * A353427 A121016 A246701

Adjacent sequences: A281639 A281640 A281641 * A281643 A281644 A281645

Keyword

nonn,more,hard

Author

Robert Price, Jan 25 2017

Extensions

a(26)-a(29) from Robert Price, Oct 13 2018

Status

approved