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A175117 Numbers n such that Sum_(i=1..n) p(i)*(-1)^(i+1) = c^2. p(i) i-th prime,c an integer. 1

%I

%S 3,9,55,181,215,459,1361,1417,1623,2047,2445,4685,6687,7353,7785,7925,

%T 8489,10333,10515,11179,14087,15227,15829

%N Numbers n such that Sum_(i=1..n) p(i)*(-1)^(i+1) = c^2. p(i) i-th prime,c an integer.

%C Numbers n such that (-1)^n*A008347(n) is a perfect square. [From _R. J. Mathar_, Feb 21 2010]

%H Harvey P. Dale, <a href="/A175117/b175117.txt">Table of n, a(n) for n = 1..300</a>

%e 2-3+5=4 thus a(1)=3 2-3+5-7+11-13+17-19+23=16 thus a(2)=9

%t Flatten[Position[Accumulate[Times@@@Partition[Riffle[Prime[Range[ 20000]], {1,-1},{2,-1,2}],2]],_?(IntegerQ[Sqrt[#]]&)]] (* _Harvey P. Dale_, Mar 19 2013 *)

%Y A000040

%K easy,nonn

%O 1,1

%A _Ctibor O. Zizka_, Feb 14 2010

%E Six more terms from _R. J. Mathar_, Feb 21 2010

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Last modified July 9 04:51 EDT 2020. Contains 335538 sequences. (Running on oeis4.)