A239309 a(n) is the smallest k such that prime(n) divides Sum_{i=1..k} A086169(i), or 0 if no such k exists, where A086169(i) is the sum of the first i twin prime pairs.

1, 0, 2, 5, 3, 37, 21, 29, 67, 71, 23, 11, 15, 7, 58, 12, 41, 8, 66, 25, 35, 370, 35, 17, 75, 159, 198, 30, 37, 153, 232, 333, 170, 507, 108, 279, 41, 61, 486, 9, 194, 211, 29, 73, 173, 575, 152, 214, 10, 147, 126, 672, 388, 77, 358, 1048, 528, 291, 322, 1491

Offset: 1

Author

Michel Lagneau, Mar 15 2014

Keywords

• nonn

Comments

a(2) = 0. Proof

It is easy to see that A054735(1)= 8 ==2 (mod 3) and A054735(n)==0 mod 3 for n > 1 where A054735 is the sum of twin pairs. Hence A086169(n)==2 (mod 3) and the prime 3 is never a divisor of A086169(n).

Examples

			a(1)=1 because A086169(1)=(3+5)=8 and prime(1)= 2 divides 8;
a(2)=0 because prime(2)=3 is never a divisor of A086169(n);
a(3)=2 because A086169(2)=(3+5)+(5+7)=20 and prime(3)= 5 divides 20.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A054735, A086169.

Programs

Mathematica

Transpose[With[{aprs=Thread[{Range[5000],Accumulate[Select[Table[Prime[n]+1,{n,45900}],PrimeQ[#+1]&]*2]}]},Flatten[Table[Select[aprs,Divisible[Last[#],Prime[m]]&,1],{m,1,60}],1]]][[1]]