A295395 Numbers k such that (61*10^k - 1)/3 is prime.

3, 17, 18, 30, 78, 98, 371, 947, 1085, 1560, 1607, 2145, 4310, 4637, 16674, 17148, 25209, 27929, 33491, 74189, 124809, 142446

Offset

1,1

Comments

Numbers such that the digits 20 followed by k occurrences of the digit 3 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 203w.

Example

3 is in this sequence because (61*10^3 - 1)/3 = 20333 is prime.
Initial terms and primes associated:
a(1) = 3, 20333;
a(2) = 17, 2033333333333333333;
a(3) = 18, 20333333333333333333;
a(4) = 30, 20333333333333333333333333333333;  etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(61*10^# - 1)/3] &]

Prog

(PARI) isok(k) = isprime((61*10^k - 1)/3); \\ Michel Marcus, Nov 22 2017

Crossrefs

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

Sequence in context: A059189 A043066 A293764 * A246143 A101144 A038886

Adjacent sequences: A295392 A295393 A295394 * A295396 A295397 A295398

Keyword

nonn,more,hard

Author

Robert Price, Nov 21 2017

Extensions

a(21)-a(22) from Robert Price, Jan 05 2020

Status

approved