A280239 Numbers k such that (16*10^k + 53)/3 is prime.

0, 1, 3, 8, 12, 14, 25, 27, 33, 60, 87, 129, 171, 339, 429, 1065, 1080, 1462, 2565, 3568, 3577, 5139, 5763, 12235, 29748, 94822, 194536

Offset

1,3

Comments

For k>1, numbers such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 51 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 53w51.

Example

3 is in this sequence because (16*10^3 + 53) / 3 = 5351 is prime.
Initial terms and primes associated:
a(1) = 0, 23;
a(2) = 1, 71;
a(3) = 3, 5351;
a(4) = 8, 533333351;
a(5) = 12, 5333333333351; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(16*10^# + 53) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((16*10^n + 53)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A331069 A161517 A255199 * A344345 A310284 A296368

Adjacent sequences: A280236 A280237 A280238 * A280240 A280241 A280242

Keyword

nonn,more,hard

Author

Robert Price, Dec 29 2016

Extensions

a(27) from Robert Price, Mar 08 2019

Status

approved