A282383 Numbers k such that (14*10^k - 221)/9 is prime.

2, 3, 15, 17, 21, 38, 93, 323, 410, 413, 444, 884, 1836, 2192, 3527, 4700, 6260, 6944, 8229, 10320, 27480, 31425, 32937, 108545, 155024, 182177, 196965

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 5 followed by the digits 31 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 15w31.

Example

3 is in this sequence because (14*10^3 - 221)/9 = 1531 is prime.
Initial terms and associated primes:
a(1) = 2, 131;
a(2) = 3, 1531;
a(3) = 15, 1555555555555531;
a(4) = 17, 155555555555555531;
a(5) = 21, 1555555555555555555531; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(14*10^# - 221)/9] &]

Prog

(PARI) isok(k) = ispseudoprime((14*10^k - 221)/9); \\ Altug Alkan, Apr 12 2018

Crossrefs

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

Sequence in context: A238691 A241721 A066491 * A299486 A173334 A331089

Adjacent sequences: A282380 A282381 A282382 * A282384 A282385 A282386

Keyword

nonn,more,hard

Author

Robert Price, Feb 13 2017

Extensions

a(24)-a(27) from Robert Price, Apr 12 2018

Status

approved