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Numbers k such that Sum_(i=1..k) prime(i)*(-1)^(i+1) is a square.
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%I #8 Feb 14 2021 16:26:10

%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 k such that Sum_(i=1..k) prime(i)*(-1)^(i+1) is a square.

%C Numbers k such that (-1)^k*A008347(k) is a perfect square. - _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;

%e 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 Cf. 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