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A076305 Numbers n such that prime(n) + prime(n+1) + prime(n+2) is a square. 9
6, 12, 59, 65, 112, 965, 1029, 1455, 1706, 1830, 1890, 2573, 3457, 4490, 4664, 5609, 7927, 9130, 10078, 10143, 12597, 18248, 19727, 20086, 20887, 21708, 22739, 25041, 26536, 28511, 29346, 29664, 29774, 33387, 39945, 40677, 46136, 49869, 58135 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that n^2 is a sum of three successive primes in A076304.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..600

EXAMPLE

6 is OK because p(6)+p(7)+p(8)=13+17+19=49=7^2.

MATHEMATICA

Select[Range[60000], IntegerQ[Sqrt[Sum[Prime[k], {k, #, # + 2}]]] &] (* Ray Chandler, Sep 26 2006 *)

Position[Partition[Prime[Range[60000]], 3, 1], _?(IntegerQ[Sqrt[ Total[ #]]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Sep 28 2018 *)

PROG

(PARI) n=0; p=2; q=3; forprime(r=5, 1e9, n++; if(issquare(p+q+r), print1(n", ")); p=q; q=r) \\ Charles R Greathouse IV, Apr 07 2017

CROSSREFS

Cf. A076304 (square roots of sums), A080665 (squares=sums), A206279 (the primes).

Cf. A064397 (2 primes), A072849 (4 primes), A166255 (70 primes), A166261 (120 primes).

Sequence in context: A324529 A076722 A322288 * A088944 A033931 A228847

Adjacent sequences:  A076302 A076303 A076304 * A076306 A076307 A076308

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 05 2002

EXTENSIONS

Corrected by Ray Chandler, Sep 26 2006

STATUS

approved

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Last modified October 17 11:59 EDT 2019. Contains 328110 sequences. (Running on oeis4.)