A272999 Numbers k such that (11*10^k + 49)/3 is prime.

1, 2, 4, 5, 7, 10, 11, 16, 18, 21, 22, 30, 41, 69, 83, 128, 166, 190, 262, 263, 353, 496, 1398, 1793, 2806, 9722, 15733, 32420, 61095, 77909, 110496

Offset

1,2

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 83 is prime (see Example section).

a(32) > 3*10^5.

Links

Table of n, a(n) for n=1..31.

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

Makoto Kamada, Search for 36w83.

Example

4 is in this sequence because (11*10^4 + 49)/3 = 36683 is prime.
Initial terms and associated primes:
a(1) = 1, 53;
a(2) = 2, 383:
a(3) = 4, 36683;
a(4) = 5, 366683;
a(5) = 7, 36666683, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(11*10^# + 49)/3] &]

Prog

(PARI) is(n)=ispseudoprime((11*10^n + 49)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A153766 A319301 A093013 * A278490 A188029 A187951

Adjacent sequences: A272996 A272997 A272998 * A273000 A273001 A273002

Keyword

nonn,more

Author

Robert Price, May 12 2016

Extensions

a(31) from Robert Price, Jul 19 2018

Status

approved