A271822 Numbers k such that (91*10^k + 11)/3 is prime.

1, 2, 4, 6, 12, 13, 14, 17, 19, 31, 50, 58, 81, 87, 161, 234, 244, 482, 505, 676, 1111, 1707, 1929, 2695, 3819, 7708, 28958, 44652, 51508, 56892, 158862, 160249, 162410

Offset: 1

Author

Robert Price, Apr 14 2016

Keywords

• nonn
• more

Comments

Numbers k such that the digits 30 followed by k-1 occurrences of the digit 3 followed by the digit 7 is prime (see Example section).

a(34) > 3*10^5.

Examples

			4 is in this sequence because (91*10^4+11)/3 = 303337 is prime.
Initial terms and associated primes:
a(1) = 1, 307;
a(2) = 2, 3037;
a(3) = 4, 303337;
a(4) = 6, 30333337;
a(5) = 12, 30333333333337, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 303w7.

Crossrefs

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

Programs

Magma

[n: n in [1..300] |IsPrime((91*10^n + 11) div 3)]; // Vincenzo Librandi, Apr 15 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(91*10^# + 11)/3] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime((91*10^n + 11)/3), print1(n, ", "))); \\ Altug Alkan, Apr 14 2016

Extensions

a(31)-a(33) from Robert Price, Feb 15 2020