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A166255 Numbers n with property that sum of 70 successive primes starting with n-th prime is a square. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sum(prime(k),k=n,n+69)=s^2; corresponding values of s: 200, 322, 770, 982, 2848, 5552, 6622, 7236, 7292, 7972, 8472, 8750, 9166 (A166256).

LINKS

Table of n, a(n) for n=1..33.

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: A142808 A101110 A142893 * A142076 A096698 A159472

Adjacent sequences:  A166252 A166253 A166254 * A166256 A166257 A166258

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 10 2009

STATUS

approved

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Last modified April 23 05:11 EDT 2014. Contains 240912 sequences.