A282635 Numbers k such that (11*10^k - 131)/3 is prime.

3, 9, 10, 28, 41, 58, 62, 86, 192, 209, 566, 1227, 1566, 1995, 2003, 3654, 4271, 6107, 6281, 8997, 24412, 32970, 65944, 85782, 112742, 115910, 141718

Offset

1,1

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 23 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 36w23.

Example

3 is in this sequence because (11*10^3 - 131)/3 = 3623 is prime.
Initial terms and associated primes:
a(1) = 3, 3623;
a(2) = 9, 3666666623;
a(3) = 10, 36666666623;
a(4) = 28, 36666666666666666666666666623;
a(5) = 41, 366666666666666666666666666666666666666623; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(11*10^# - 131)/3] &]

Crossrefs

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

Sequence in context: A340387 A025616 A305091 * A308084 A136852 A031115

Adjacent sequences: A282632 A282633 A282634 * A282636 A282637 A282638

Keyword

nonn,more,hard,changed

Author

Robert Price, Feb 23 2017

Extensions

a(25)-a(27) from Robert Price, Sep 28 2018

Status

approved