A280381 Numbers k such that (17*10^k + 31)/3 is prime.

1, 2, 5, 6, 8, 12, 13, 14, 19, 61, 127, 137, 173, 175, 305, 540, 617, 935, 1398, 1834, 3295, 4351, 9188, 10808, 39409, 57325, 63798, 67091, 183764, 194502, 196921, 288692

Offset

1,2

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 77 is prime (see Example section).

a(33) > 3*10^5. - Robert Price, Jul 10 2023

Links

Table of n, a(n) for n=1..32.

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

Makoto Kamada, Search for 56w77.

Example

5 is in this sequence because (17*10^5 + 31) / 3 = 566677 is prime.
Initial terms and associated primes:
a(1) = 1, 67;
a(2) = 2, 577;
a(3) = 5, 566677;
a(4) = 6, 5666677;
a(5) = 8, 5333333333351; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(17*10^# + 31) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((17*10^n + 31)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A300063 A230902 A243680 * A333965 A105107 A002253

Adjacent sequences: A280378 A280379 A280380 * A280382 A280383 A280384

Keyword

nonn,more,hard

Author

Robert Price, Jan 01 2017

Extensions

a(29)-a(31) from Robert Price, Jan 29 2019

a(32) from Robert Price, Jul 10 2023

Status

approved