A309774 Numbers k such that 5*10^k + 11 is prime.

1, 3, 6, 35, 51, 84, 123, 1589, 1591, 4911, 6221, 48645, 78504, 107355

Offset

1,2

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 11 is prime (see Example section).

a(15) > 2*10^5.

Links

Table of n, a(n) for n=1..14.

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

Makoto Kamada, Search for 50w11.

Example

6 is in this sequence because 5*10^4 + 11 = 5000011 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 3, 5011;
a(3) = 6, 5000011;
a(4) = 35, 500000000000000000000000000000000011; etc.

Mathematica

Select[Range[0, 200000], PrimeQ[5*10^# + 11] &]

Crossrefs

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

Sequence in context: A308557 A134748 A068904 * A244296 A143046 A246069

Adjacent sequences: A309771 A309772 A309773 * A309775 A309776 A309777

Keyword

nonn,more,hard

Author

Robert Price, Aug 16 2019

Status

approved