This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A072849 #35 Jun 28 2024 04:26:47
%S A072849 3,21,33,84,104,199,689,1848,1923,3435,3795,3985,4126,4742,5968,6413,
%T A072849 6495,7649,8927,9906,16885,17677,20474,20996,22924,23923,36902,38733,
%U A072849 40347,40654,41956,42601,43047,44482,44920,51608,52305,56706,66032
%N A072849 Prime(a(n)) + ... + prime(a(n)+3) is a square = A051395(n)^2.
%C A072849 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 A072849 Amiram Eldar, <a href="/A072849/b072849.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..200 from Harvey P. Dale)
%F A072849 a(n) = A000720(A206280(n)). - _Amiram Eldar_, Jun 28 2024
%e A072849 a(1) = 3 because prime(3) + prime(4) + prime(5) + prime(6) = 5+7+11+13 = 36 = 6*6.
%t A072849 Flatten[Position[Partition[Prime[Range[70000]],4,1],_?(IntegerQ[ Sqrt[ Total[ #]]]&),{1},Heads->False]] (* _Harvey P. Dale_, Dec 09 2015 *)
%o A072849 (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 A072849 Cf. A051395 (square root of sums), A206280 (primes), A000720.
%Y A072849 Cf. A064397 (2 primes), A076305 (3 primes), A166255 (70 primes), A166261 (120 primes).
%K A072849 easy,nonn
%O A072849 1,1
%A A072849 _Zak Seidov_, Jun 21 2003
%E A072849 Definition corrected by _Zak Seidov_, Dec 13 2014