A294916 Numbers k such that (10^k + 191)/3 is prime.

1, 2, 3, 6, 7, 13, 18, 33, 39, 126, 154, 168, 213, 4150, 4153, 5658, 6394, 21993, 29674, 38936, 47095, 94096, 135174, 139398

Offset

1,2

Comments

For k > 1, numbers such that k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).

a(25) > 2*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 3w97

Example

2 is in this sequence because (10^2 + 191)/3 = 97 is prime.
Initial terms and primes associated:
a(1) = 1, 67;
a(2) = 2, 97;
a(3) = 3, 397;
a(4) = 6, 333397;
a(5) = 7, 3333397; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(10^# + 191)/3] &]

Crossrefs

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

Sequence in context: A330145 A183558 A328164 * A233423 A328024 A309815

Adjacent sequences: A294913 A294914 A294915 * A294917 A294918 A294919

Keyword

nonn,more,hard

Author

Robert Price, Nov 10 2017

Extensions

a(23)-a(24) from Robert Price, Feb 14 2018

Status

approved