A166255 Numbers k with property that the sum of 70 successive primes starting with prime(k) is a square.

71, 201, 1024, 1594, 10915, 36934, 51050, 60054, 60914, 71822, 80331, 85230, 92916, 96352, 103271, 114667, 151019, 158591, 183484, 184348, 193979, 196078, 223587, 277476, 295890, 309502, 317601, 334181, 338139, 369101, 485330, 494188, 530832

Offset

1,1

Comments

Sum_{i=k..k+69} prime(i) = s^2; and the values of s are A166256.

Links

David A. Corneth, Table of n, a(n) for n = 1..693 (first 100 terms from Zak Seidov)

Example

prime(71)+...+prime(71+69) = 200^2 = A166256(1)^2,
prime(201)+...+prime(201+69) = 322^2 = A166256(2)^2,
prime(1024)+...+prime(1024+69) = 770^2 = A166256(3)^2.

Mathematica

PrimePi[First[#]]&/@Select[Partition[Prime[Range[1000000]], 70, 1], IntegerQ[ Sqrt[ Total[#]]]&] (* Harvey P. Dale, Jun 13 2011 *)

Crossrefs

Cf. A166256.

Cf. A064397 (2 primes), A076305 (3 primes), A072849 (4 primes), A166261 (120 primes).

Sequence in context: A101110 A142893 A245945 * A142076 A096698 A159472

Adjacent sequences: A166252 A166253 A166254 * A166256 A166257 A166258

Keyword

nonn,less

Author

Zak Seidov, Oct 10 2009

Status

approved