A275284 Numbers k such that (29*10^k - 41)/3 is prime.

1, 2, 5, 7, 13, 16, 55, 61, 65, 98, 134, 296, 354, 527, 901, 1206, 1916, 2899, 3725, 4709, 7529, 8942, 12050, 12880, 15516, 25976, 62030, 111020, 195648, 197941

Offset: 1

Author

Robert Price, Jul 21 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 6 followed by the digits 53 is prime (see Example section).

a(31) > 2*10^5.

Examples

			5 is in this sequence because (29*10^5 - 41)/3 = 966653 is prime.
Initial terms and associated primes:
a(1) = 1, 83;
a(2) = 2, 953;
a(3) = 5, 966653;
a(4) = 7, 96666653;
a(5) = 13, 96666666666653, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 96w53.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(29*10^# - 41)/3] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime((29*10^n-41)/3), print1(n, ", "))); \\ Altug Alkan, Jul 21 2016

Extensions

a(28)-a(30) from Tyler Busby, Mar 20 2024