A293534 Numbers k such that 22*10^k + 3 is prime.

1, 2, 3, 6, 15, 18, 26, 51, 54, 68, 85, 242, 597, 2335, 3463, 4160, 5565, 8322, 11389, 43982, 70729, 127645, 151998

Offset

1,2

Comments

For k > 0, numbers k such that the digits 22 followed by k-1 occurrences of the digit 0 followed by the digit 3 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 220w3.

Example

2 is in this sequence because 22*10^2 + 3 = 2203 is prime.
Initial terms and associated primes:
a(1) = 1, 223;
a(2) = 2, 2203;
a(3) = 3, 22003;
a(4) = 6, 22000003;
a(5) = 15, 22000000000000003; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[22*10^# + 3] &]

Prog

(PARI) isok(k) = isprime(22*10^k + 3); \\ Altug Alkan, Oct 11 2017

Crossrefs

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

Sequence in context: A335260 A090983 A198684 * A066653 A081945 A329745

Adjacent sequences: A293531 A293532 A293533 * A293535 A293536 A293537

Keyword

nonn,more,hard

Author

Robert Price, Oct 11 2017

Extensions

a(22)-a(23) from Robert Price, Jan 04 2020

Status

approved