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A086448 a(n) = the least integer of the form [prime(n+1)+prime(n+2)+...+prime(n+k)]/prime(n). 3

%I

%S 4,4,18,16,12,12,6,16,6,102,11,93,119,345,48,240,138,100,263,19,227,

%T 282,31,1071,11,126,386,278,184,642,164,445,55,213,89,190,895,1120,61,

%U 258,4629,323,122,789,5226,59,1292,325,364,374,430,3939,118,695,87,73,358

%N a(n) = the least integer of the form [prime(n+1)+prime(n+2)+...+prime(n+k)]/prime(n).

%C It seems that a(n) exists for any n.

%C Among first 1000 terms, the largest term is a(793) = 1807606, with p = prime(793) = 6079, and 6079*1807606 = the sum of 42840 consecutive primes after p. - _Zak Seidov_, Nov 07 2014

%C Among first 10000 terms, the largest term is a(9349) = 30376745, with p = prime(9349) = 97159, and p*(9349) = the sum of 629543 consecutive primes after p: 2951374167455 = sum(prime(k), k = 9349 + 1..9349 + 629543) - _Zak Seidov_, Feb 21 2015

%H Zak Seidov, <a href="/A086448/b086448.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3)=18 because prime(3)=5 and (7+11+13+17+19+23)/5 = 18.

%t bb={}; Do[s0=Prime[n0]; s=0; Do[If[IntegerQ[ss0=(s+=Prime[n])/s0], bb=Append[bb, ss0]; Break[]], {n, n0+1, 8000}], {n0, 1, 10}]; bb

%Y Cf. A055233, A055514, A086447.

%K easy,nonn

%O 1,1

%A _Zak Seidov_, Jul 20 2003

%E Edited by _Don Reble_, Nov 10 2005

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Last modified November 20 13:19 EST 2019. Contains 329336 sequences. (Running on oeis4.)