A278591 Numbers k such that (11*10^k - 107) / 3 is prime.

2, 3, 5, 7, 8, 11, 14, 18, 25, 39, 81, 91, 347, 391, 438, 464, 539, 818, 1051, 1125, 1598, 3384, 11966, 79867, 147313

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 31 is prime (see Example section).

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 36w31.

Example

3 is in this sequence because (11*10^3 - 107) / 3 = 3631 is prime.
Initial terms and primes associated:
a(1) = 2, 331;
a(2) = 3, 3631;
a(3) = 5, 366631;
a(4) = 7, 36666631;
a(5) = 8, 366666631; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(11*10^# - 107) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((11*10^n - 107)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A186285 A190855 A190810 * A191121 A026401 A069353

Adjacent sequences: A278588 A278589 A278590 * A278592 A278593 A278594

Keyword

nonn,more,hard

Author

Robert Price, Nov 23 2016

Extensions

First comment and second link corrected by Robert Price, May 23 2018

a(25) from Robert Price, Sep 30 2018

Status

approved