A137368 a(n) = least m such that sum of m reciprocal primes starting with n-th prime is >1.

3, 9, 27, 66, 144, 253, 424, 651, 977, 1392, 1866, 2479, 3169, 3981, 4978, 6137, 7420, 8829, 10477, 12279, 14295, 16613, 19124, 21906, 24904, 28056, 31494, 35320, 39486, 44102, 49116, 54103, 59468, 65143, 71315, 77649, 84504, 91720, 99303, 107365

Offset: 1

Author

Zak Seidov, Apr 09 2008

Keywords

• nonn

Examples

			a(1)=3 because 1/2+1/3+1/5=31/30 (3 terms), while 1/2+1/3<1,
a(2)=9 because 1/3+1/5+1/7+1/11+1/13+1/17+1/19+1/23+1/29 =3343015913/3234846615 (9 terms), while 1/3+...+1/23<1,
a(3)=27 because 1/p(3)+...1/p(29)>1 (27 terms) while 1/p(3)+...1/p(28)<1.
		

Programs

Mathematica

ss={};Do[s=1/Prime[n];k=1;While[s<1,k++;s+=1/Prime[n+k-1]];AppendTo[ss,k],{n,1,30}]

Formula

a(n)=m: Sum_{i=n..n+m-1} 1/prime(i) > 1, while Sum_{i=n..n+m-2} 1/prime(i) < 1.

Extensions

a(31)-a(40) from Donovan Johnson, Sep 05 2008