A293034 Numbers k such that (203*10^k + 1)/3 is prime.

1, 5, 12, 17, 21, 23, 25, 29, 109, 168, 195, 327, 417, 461, 1991, 3512, 3955, 4239, 6228, 24317, 91613, 131457, 152143, 159381, 162689

Offset

1,2

Comments

For k > 0, numbers k such that the digits 67 followed by k-1 occurrences of the digit 6 followed by the digit 7 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 676w7.

Example

5 is in this sequence because (203*10^5 + 1)/3 = 6766667 is prime.
Initial terms and associated primes:
a(1) = 1, 677;
a(2) = 5, 6766667;
a(3) = 12, 67666666666667;
a(4) = 17, 6766666666666666667;
a(5) = 21, 67666666666666666666667; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(203*10^# + 1)/3] &]

Crossrefs

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

Sequence in context: A269753 A270133 A314284 * A314285 A089988 A314286

Adjacent sequences: A293031 A293032 A293033 * A293035 A293036 A293037

Keyword

nonn,more,hard

Author

Robert Price, Sep 28 2017

Extensions

a(22)-a(25) from Robert Price, Mar 22 2020

Status

approved