A293757 Numbers k such that (10^k - 97)/3 is prime.

4, 5, 7, 13, 16, 22, 30, 56, 78, 80, 90, 194, 316, 1796, 2004, 3856, 5226, 6737, 10841, 43638, 50467, 85666

Offset

1,1

Comments

For k > 1, numbers k such that k-2 occurrences of the digit 3 followed by the digits 01 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 3w01.

Example

4 is in this sequence because (10^4 - 97)/3 = 3301 is prime.
Initial terms and associated primes:
a(1) = 4, 3301;
a(2) = 5, 33301;
a(3) = 7, 3333301;
a(4) = 13, 3333333333301;
a(5) = 16, 3333333333333301; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(10^# - 97)/3] &]

Prog

(Magma) [n: n in [1..400] |IsPrime((10^n-97) div 3)]; // Vincenzo Librandi, Oct 16 2017

Crossrefs

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

Sequence in context: A048224 A064237 A139373 * A275273 A069575 A250182

Adjacent sequences: A293754 A293755 A293756 * A293758 A293759 A293760

Keyword

nonn,more,hard

Author

Robert Price, Oct 15 2017

Extensions

Example and Link corrected by Robert Price, Nov 22 2017

Status

approved