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%I #27 Nov 13 2022 09:39:07
%S 3,21,33,84,104,199,689,1848,1923,3435,3795,3985,4126,4742,5968,6413,
%T 6495,7649,8927,9906,16885,17677,20474,20996,22924,23923,36902,38733,
%U 40347,40654,41956,42601,43047,44482,44920,51608,52305,56706,66032
%N Prime(a(n))+...+prime(a(n)+3) is a square = A051395(n)^2.
%C Conjecture: this sequence and A064397 are disjoint. That is to say, prime(n) + prime(n+1) and prime(n) + prime(n+1) + prime(n+2) + prime(n+3) cannot be squares at the same time. - _Jianing Song_, Nov 13 2022
%H Harvey P. Dale, <a href="/A072849/b072849.txt">Table of n, a(n) for n = 1..200</a>
%e a(1)=3 because prime(3)+prime(4)+prime(5)+prime(6) = 5+7+11+13 = 36 = 6*6.
%t Flatten[Position[Partition[Prime[Range[70000]],4,1],_?(IntegerQ[ Sqrt[ Total[ #]]]&),{1},Heads->False]] (* _Harvey P. Dale_, Dec 09 2015 *)
%o (PARI) lista(m) = {for (n = 1, m, if (issquare(prime(n) + prime(n+1) + prime(n+2) + prime(n+3)), print1(n, ", ")););} \\ _Michel Marcus_, Apr 19 2013
%Y Cf. A051395 (square root of sums), A206280 (primes).
%Y Cf. A064397 (2 primes), A076305 (3 primes), A166255 (70 primes), A166261 (120 primes).
%K easy,nonn
%O 1,1
%A _Zak Seidov_, Jun 21 2003
%E Definition corrected by _Zak Seidov_, Dec 13 2014
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