A282895 Numbers k such that (11*10^k + 91)/3 is prime.

1, 2, 3, 4, 5, 7, 9, 15, 27, 29, 39, 62, 77, 106, 114, 357, 555, 962, 1013, 2372, 8235, 16047, 82323, 294308

Offset

1,2

Comments

For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 97 is prime (see Example section).

a(25) > 3*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 36w97.

Example

3 is in this sequence because (11*10^3 + 91)/3 = 3697 is prime.
Initial terms and primes associated:
a(1) = 1, 67;
a(2) = 2, 397;
a(3) = 3, 3697;
a(4) = 4, 36697;
a(5) = 5, 366697; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(11*10^# + 91)/3] &]

Crossrefs

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

Sequence in context: A263360 A050763 A252023 * A293535 A261170 A051453

Adjacent sequences: A282892 A282893 A282894 * A282896 A282897 A282898

Keyword

nonn,more,hard

Author

Robert Price, Feb 24 2017

Extensions

a(24) from Robert Price, Jul 12 2023

Status

approved