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%I #18 Sep 18 2022 11:13:53
%S 13,37,277,313,613,7591,8209,12157,14557,15679,16267,23053,32233,
%T 42953,44887,55213,81013,94687,105649,106397,135241,203317,221401,
%U 225769,235747,245941,258707,287671,306541,331333,342049,346111,347443,393853,479191,488827
%N Smallest of three consecutive primes whose sum is a square.
%H Charles R Greathouse IV, <a href="/A206279/b206279.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000040(A076305(n)). - _Zak Seidov_, Apr 07 2017
%e a(4) = 313. The next two primes are 317 and 331, and 313 + 317 + 331 = 961 = 31^2.
%t Transpose[Select[Partition[Prime[Range[50000]],3,1],IntegerQ[ Sqrt[ Total[#]]]&]][[1]]
%o (PARI) p=2;q=3;forprime(r=5,1e9,if(issquare(p+q+r),print1(p", "));p=q;q=r) \\ _Charles R Greathouse IV_, Aug 28 2013
%Y Cf. A000040, A061275, A076304, A076305, A206280, A206281.
%K nonn
%O 1,1
%A _Harvey P. Dale_, Feb 05 2012