A202606 a(n) = ceiling(((10^n - 1)^2/9 + 10^n)/18).

1, 2, 67, 6217, 617717, 61732717, 6172882717, 617284382717, 61728399382717, 6172839549382717, 617283951049382717, 61728395066049382717, 6172839506216049382717, 617283950617716049382717, 61728395061732716049382717, 6172839506172882716049382717

Offset: 0

Author

Arkadiusz Wesolowski, Dec 21 2011

Keywords

• easy
• nonn

Comments

a(n) are distinct primes for n = 1 to 8.

Examples

			a(2) = 67 because (99^2/9 + 100)/18 = 66.05555....
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 0..100
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 8
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A000217, A002275, A084849.

Programs

Magma

[ ((10^n-1)^2/9+10^n-1)/18+1 : n in [0..15]];

Maple

seq(((10^n-1)^2/9+10^n-1)/18+1, n=0..15);

Mathematica

Table[a = (10^n - 1)/18; 2*a^2 + a + 1, {n, 0, 15}]
LinearRecurrence[{111,-1110,1000},{1,2,67},20] (* Harvey P. Dale, Jul 07 2017 *)

PARI

for(n=0, 15, print1(((10^n-1)^2/9+10^n-1)/18+1, ", "))

Formula

a(n) = ceiling(((10^n - 1)^2/9 + 10^n)/18).

a(n) = (10^n - 1)*((10^n - 1)/9 + 1)/18 + 1.

G.f.: (1 - 109*x + 955*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).