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%I #26 Sep 08 2022 08:45:07
%S 6,12,59,65,112,965,1029,1455,1706,1830,1890,2573,3457,4490,4664,5609,
%T 7927,9130,10078,10143,12597,18248,19727,20086,20887,21708,22739,
%U 25041,26536,28511,29346,29664,29774,33387,39945,40677,46136,49869,58135
%N Numbers n such that prime(n) + prime(n+1) + prime(n+2) is a square.
%C See A076304 for the square roots of the sums of the three primes.
%H Harvey P. Dale, <a href="/A076305/b076305.txt">Table of n, a(n) for n = 1..600</a>
%F a(n) = A000720(A206279(n)). - _M. F. Hasler_, Jan 03 2020
%e 6 is in the sequence because prime(6) + prime(7) + prime(8) = 13 + 17 + 19 = 49 = 7^2.
%t Select[Range[60000], IntegerQ[Sqrt[Sum[Prime[k], {k, #, # + 2}]]] &] (* _Ray Chandler_, Sep 26 2006 *)
%t Position[Partition[Prime[Range[60000]],3,1],_?(IntegerQ[Sqrt[ Total[ #]]]&), 1,Heads->False]//Flatten (* _Harvey P. Dale_, Sep 28 2018 *)
%o (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
%o (Magma) [k:k in [1..60000]| IsSquare(&+[NthPrime(k+m):m in [0,1,2]])]; // _Marius A. Burtea_, Jan 04 2020
%Y Cf. A076304 (square roots of sums), A080665 (squares = sums), A206279 (lesser of the primes).
%Y Cf. A064397 (same for 2 primes), A072849 (4 primes), A166255 (70 primes), A166261 (120 primes).
%K nonn
%O 1,1
%A _Zak Seidov_, Oct 05 2002
%E Corrected by _Ray Chandler_, Sep 26 2006
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