A282358 Numbers k such that (182*10^k + 1)/3 is prime.

0, 1, 2, 6, 8, 12, 15, 19, 30, 31, 110, 175, 358, 456, 475, 1359, 1741, 2061, 6062, 7568, 10027, 10732, 27761, 52018, 75456, 133543, 136291, 203048

Offset

1,3

Comments

For k > 1, numbers k such that the digits 60 followed by k-1 occurrences of the digit 6 followed by the digit 7 is prime (see Example section).

a(29) > 3*10^5.

Links

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

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

Makoto Kamada, Search for 606w7.

Example

2 is in this sequence because (182*10^2 + 1)/3 = 6067 is prime.
Initial terms and associated primes:
a(1) = 0, 61;
a(2) = 1, 607;
a(3) = 2, 6067;
a(4) = 6, 60666667;
a(5) = 8, 6066666667; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(182*10^# + 1)/3] &]

Crossrefs

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

Sequence in context: A189515 A190344 A287000 * A064796 A304483 A268177

Adjacent sequences: A282355 A282356 A282357 * A282359 A282360 A282361

Keyword

nonn,more,hard

Author

Robert Price, Feb 13 2017

Extensions

a(26)-a(27) from Robert Price, Feb 27 2020

a(28) from Robert Price, Oct 25 2023

Status

approved