A175117 Numbers k such that Sum_(i=1..k) prime(i)*(-1)^(i+1) is a square.

3, 9, 55, 181, 215, 459, 1361, 1417, 1623, 2047, 2445, 4685, 6687, 7353, 7785, 7925, 8489, 10333, 10515, 11179, 14087, 15227, 15829

Offset: 1

Author

Ctibor O. Zizka, Feb 14 2010

Keywords

• easy
• nonn

Comments

Numbers k such that (-1)^k*A008347(k) is a perfect square. - R. J. Mathar, Feb 21 2010

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000040.

Programs

Mathematica

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

Extensions

Six more terms from R. J. Mathar, Feb 21 2010