A289751 Numbers k such that (4*10^k + 137)/3 is prime.

0, 1, 2, 5, 8, 13, 18, 31, 42, 43, 48, 53, 210, 792, 1324, 1868, 2544, 5609, 10210, 10514, 11232, 14731, 36583, 50060, 128510, 198268

Offset

1,3

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 79 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 13w79.

Example

5 is in this sequence because (4*10^5 + 137)/3 = 179 is prime.
Initial terms and associated primes:
a(1) = 0, 47;
a(2) = 1, 59;
a(3) = 2, 179;
a(4) = 5, 133379;
a(5) = 8, 133333379; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(4*10^# + 137)/3] &]

Crossrefs

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

Sequence in context: A054074 A290268 A000982 * A200274 A122221 A083704

Adjacent sequences: A289748 A289749 A289750 * A289752 A289753 A289754

Keyword

nonn,more,hard

Author

Robert Price, Jul 11 2017

Extensions

a(25)-a(26) from Robert Price, Mar 21 2018

Status

approved