A280557 Numbers k such that (11*10^k - 113) / 3 is prime.

4, 6, 13, 15, 23, 25, 31, 71, 133, 333, 341, 905, 1027, 3667, 7241, 8217, 8493, 9816, 11842, 15454, 15891, 19117, 30424, 35196, 42808, 78408, 95641, 177466

Offset

1,1

Comments

For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 29 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 36w29.

Example

6 is in this sequence because (11*10^6 - 113) / 3 = 3666629 is prime.
Initial terms and primes associated:
a(1) = 4, 36629;
a(2) = 6, 3666629;
a(3) = 13, 36666666666629;
a(4) = 15, 3666666666666629;
a(5) = 23, 366666666666666666666629; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(11*10^# - 113) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((11*10^n - 113)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A074165 A137821 A010061 * A266665 A249715 A249440

Adjacent sequences: A280554 A280555 A280556 * A280558 A280559 A280560

Keyword

nonn,more,hard

Author

Robert Price, Jan 05 2017

Extensions

a(28) from Robert Price, Oct 10 2018

Status

approved