A278336 Numbers k such that (94*10^k - 7) / 3 is prime.

0, 1, 4, 5, 9, 16, 20, 41, 43, 63, 127, 159, 413, 1591, 1812, 2031, 2315, 2437, 4177, 4860, 5771, 7060, 7389, 9925, 34103, 115879

Offset

1,3

Comments

For k > 0, numbers k such that the digits 31 followed by k-1 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).

a(27) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 313w1.

Example

4 is in this sequence because (94*10^4 - 7) / 3 = 313331 is prime.
Initial terms and associated primes:
a(1) = 0, 29;
a(2) = 1, 311;
a(3) = 4, 313331;
a(4) = 5, 3133331;
a(5) = 9, 31333333331; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(94*10^# - 7) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((94*10^n - 7)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A020682 A243702 A155565 * A051216 A255978 A069089

Adjacent sequences: A278333 A278334 A278335 * A278337 A278338 A278339

Keyword

nonn,more,hard

Author

Robert Price, Nov 18 2016

Extensions

a(26) from Robert Price, Mar 10 2020

Status

approved