A275978 Numbers k such that (101*10^k + 1)/3 is prime.

1, 4, 6, 12, 34, 54, 60, 61, 73, 148, 349, 552, 649, 967, 1044, 2521, 4501, 5721, 6133, 9052, 9880, 16126, 16215, 19146, 61770

Offset: 1

Author

Robert Price, Aug 15 2016

Keywords

• nonn
• more

Comments

Numbers k such that the digits 33 followed by k-1 occurrences of the digit 6 followed by the digit 7 is prime (see Example section).

a(26) > 10^5.

Examples

			4 is in this sequence because (101*10^4 + 1)/3 = 336667 is prime.
Initial terms and associated primes:
a(1) = 1, 337;
a(2) = 4, 336667;
a(3) = 6, 33666667;
a(4) = 12, 33666666666667;
a(5) = 34, 336666666666666666666666666666666667, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 336w7.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(101*10^# + 1)/3] &]

PARI

isok(n) = isprime((101*10^n + 1)/3); \\ Michel Marcus, Aug 16 2016