A295328 Numbers k such that 3*10^k + 67 is prime.

1, 2, 3, 25, 61, 75, 99, 122, 145, 187, 292, 586, 1328, 2457, 3410, 4819, 5986, 6638, 20855, 28161, 47647, 49387, 67499, 72723

Offset

1,2

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 0 followed by the digits 67 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 30w67.

Example

2 is in this sequence because 3*10^2 + 67 = 367 is prime.
Initial terms and associated primes:
a(1) = 1, 97;
a(2) = 2, 367;
a(3) = 3, 3067;
a(4) = 25, 30000000000000000000000067;  etc.

Mathematica

Select[Range[0, 100000], PrimeQ[3*10^# + 67] &]

Prog

(PARI) isok(k) = isprime(3*10^k + 67); \\ Michel Marcus, Nov 20 2017

Crossrefs

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

Sequence in context: A048674 A320223 A296275 * A281169 A296281 A226018

Adjacent sequences: A295325 A295326 A295327 * A295329 A295330 A295331

Keyword

nonn,more,hard

Author

Robert Price, Nov 19 2017

Status

approved