A273924 Numbers k such that (7*10^k - 13)/3 is prime.

1, 2, 5, 6, 28, 53, 56, 86, 88, 90, 96, 136, 142, 186, 202, 373, 448, 785, 988, 1263, 1966, 3561, 4768, 9658, 9831, 17797, 42286, 49893, 98007, 129472, 146860

Offset: 1

Author

Robert Price, Jun 04 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 29 is prime (see Example section).

a(32) > 2*10^5.

Examples

			5 is in this sequence because (7*10^5 - 13)/3 = 233329 is prime.
Initial terms and associated primes:
a(1) = 1, 19;
a(2) = 2, 229;
a(3) = 5, 233329;
a(4) = 6, 2333329;
a(5) = 28, 23333333333333333333333333329, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 23w29.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# - 13)/3] &]

PARI

is(n)=ispseudoprime((7*10^n - 13)/3) \\ Charles R Greathouse IV, Jun 08 2016

Extensions

a(30)-a(31) from Robert Price, Jul 13 2018