A294637 Numbers k such that (29*10^k - 113)/3 is prime.

1, 2, 3, 11, 27, 43, 122, 135, 218, 230, 997, 1005, 1073, 1133, 1159, 1541, 2287, 2912, 3692, 12503, 45761, 73659, 125021

Offset

1,2

Comments

For k>1, numbers such that the digit 9 followed by k-2 occurrences of the digit 6 followed by the digits 29 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 96w29.

Example

2 is in this sequence because (29*10^2 - 113)/3 = 929 is prime.
Initial terms and primes associated:
a(1) = 1, 59;
a(2) = 2, 929;
a(3) = 3, 9629;
a(4) = 11, 966666666629;
a(5) = 27, 9666666666666666666666666629; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(29*10^# - 113)/3] &]

Crossrefs

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

Sequence in context: A048412 A259428 A002981 * A295613 A232212 A232219

Adjacent sequences: A294634 A294635 A294636 * A294638 A294639 A294640

Keyword

nonn,more,hard

Author

Robert Price, Nov 05 2017

Extensions

a(23) from Robert Price, Oct 03 2019

Status

approved