A273063 Numbers k such that (112*10^k + 17)/3 is prime.

0, 1, 2, 3, 4, 8, 44, 53, 79, 89, 95, 120, 224, 259, 290, 488, 725, 821, 1815, 3096, 3100, 3404, 5909, 8054, 11879, 17298, 25588, 41516, 127324, 191900

Offset: 1

Author

Robert Price, May 14 2016

Keywords

• nonn
• more

Comments

For k > 0, numbers k such that the digits 37 followed by k-1 occurrences of the digit 3 followed by the digit 9 is prime (see Example section).

a(31) > 3*10^5.

Examples

			3 is in this sequence because (112*10^3+17)/3 = 37339 is prime.
Initial terms and associated primes:
a(1) = 0, 43;
a(2) = 1, 379:
a(3) = 2, 3739;
a(4) = 3, 37339;
a(5) = 4, 373339, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 373w9.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(112*10^# + 17)/3] &]

PARI

is(n)=ispseudoprime((112*10^n + 17)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(29)-a(30) from Robert Price, Mar 05 2020