A293683 Numbers k such that (7*10^k + 53)/3 is prime.

1, 2, 3, 7, 20, 28, 32, 35, 48, 193, 332, 359, 444, 568, 763, 1414, 10964, 13703, 15420, 27384, 49404, 62362, 65064, 104113, 187645

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 51 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 23w51.

Example

2 is in this sequence because (7*10^2 + 53)/3 = 251 is prime.
Initial terms and associated primes:
a(1) = 1, 41;
a(2) = 2, 251;
a(3) = 3, 2351;
a(4) = 7, 23333351;
a(5) = 20, 233333333333333333351; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# + 53)/3] &]

Crossrefs

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

Sequence in context: A244917 A172976 A171655 * A006073 A052402 A372076

Adjacent sequences: A293680 A293681 A293682 * A293684 A293685 A293686

Keyword

nonn,more,hard

Author

Robert Price, Oct 14 2017

Extensions

a(24)-a(25) from Robert Price, May 20 2018

Status

approved