A273002 Numbers k such that 16*10^k + 1 is prime.

0, 2, 3, 4, 18, 21, 36, 58, 68, 78, 84, 94, 150, 178, 190, 591, 686, 812, 840, 2308, 2530, 2884, 4311, 6134, 7695, 8004, 8109, 9777, 15570, 17505

Offset: 1

Author

Robert Price, May 12 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digits 16 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(31) > 10^5.

Examples

			4 is in this sequence because 16*10^4+1 = 160001 is prime.
Initial terms and associated primes:
a(1) = 0, 17;
a(2) = 2, 1601;
a(3) = 3, 16001;
a(4) = 4, 160001;
a(5) = 18, 16000000000000000001. etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 160w1.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[16*10^#+1] &]

PARI

is(n)=ispseudoprime(16*10^n+1) \\ Charles R Greathouse IV, Jun 13 2017