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 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
 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 (list; graph; refs; listen; history; text; internal format)
 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, Accumulate[Select[Table[Prime[n]+1, {n, 45900}], PrimeQ[#+1]&]*2]}]}, Flatten[Table[Select[aprs, Divisible[Last[#], Prime[m]]&, 1], {m, 1, 60}], 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

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Last modified May 16 15:56 EDT 2022. Contains 353706 sequences. (Running on oeis4.)