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

1,3

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).

Links

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

Example

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.

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]]

Crossrefs

Cf. A000040, A054735, A086169.

Sequence in context: A264137 A308949 A109734 * A077073 A307126 A191474

Adjacent sequences: A239306 A239307 A239308 * A239310 A239311 A239312

Keyword

nonn

Author

Michel Lagneau, Mar 15 2014

Status

approved