A267420 Integers k such that 19*(10^k) + 1 is prime.

1, 2, 3, 11, 18, 25, 60, 71, 85, 168, 285, 627, 872, 1092, 1101, 1169, 1974, 2011, 2135, 2405, 10147, 14029, 16121, 17501, 46548

Offset: 1

Author

Emre APARI, Jan 14 2016

Keywords

• nonn
• more

Comments

For k > 0, numbers k such that the digits 19 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(26) > 10^5.

Examples

			3 is in this sequence because 19*10^3 + 1 = 19001 is prime.
Initial terms and associated primes:
a(1) = 1, 191;
a(2) = 2, 1901;
a(3) = 3, 19001;
a(4) = 11, 1900000000001;
a(5) = 18, 19000000000000000001, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 190w1.

Programs

Maple

select(k->isprime(19*(10^k)+1),[$1..3000]); # Muniru A Asiru, Oct 07 2018

Mathematica

Select[Range[0, 100000], PrimeQ[19*10^# + 1] &]

PARI

is(n) = ispseudoprime(19*(10^n) + 1); \\ Altug Alkan, Jan 15 2016

PARI

lista(nn) = for(n=1, nn, if(isprime(19*(10^n) +1 ), print1(n, ", "))); \\ Altug Alkan, Jan 18 2016

Extensions

a(13)-a(20) from Altug Alkan, Jan 18 2016

a(21)-a(25) from Robert Price, Oct 07 2018