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 A129412 #13 Aug 01 2025 17:05:02 %S A129412 0,2,4,10,12,14,24,30,32,34,42,44,54,62,64,70,82,84,92,94,100,112,114, %T A129412 122,132,134,144,152,160,164,174,180,190,200,204,212,214,230,232,240, %U A129412 242,250,252,262,264,272,274,284,290,300,304,310,314,344,354,370,372 %N A129412 Numbers k such that mean of 7 consecutive squares starting with k^2 is prime. %C A129412 Sum of 7 consecutive squares starting with k^2 is equal to 7*(13 + 6*k + k^2) and mean is (13 + 6*k + k^2) = (k+3)^2+4. Hence a(n) = A007591(n+1)-3. %H A129412 Charles R Greathouse IV, <a href="/A129412/b129412.txt">Table of n, a(n) for n = 1..10000</a> %e A129412 (0^2+...+6^2)/7=13 prime, (2^2+...+8^2)/7=29 prime, (4^2+...+10^2)/7=53 prime. %t A129412 Select[Range[0,400],PrimeQ[Mean[Range[#,#+6]^2]]&] (* _Harvey P. Dale_, Apr 23 2011 *) %o A129412 (PARI) is(n)=isprime(n^2+6*n+13) \\ _Charles R Greathouse IV_, Jun 13 2017 %Y A129412 Cf. A005473, A056899, A067201, A007591, A129389, A098062. %K A129412 nonn,easy %O A129412 1,2 %A A129412 _Zak Seidov_, Apr 14 2007