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 A129592 #20 Jun 25 2019 01:06:26
%S A129592 2,7,13,43,53,59,127,241,271,317,331,349,367,439,487,491,607,659,719,
%T A129592 733,757,773,821,857,881,929,971,1087,1193,1259,1289,1303,1409,1427,
%U A129592 1453,1607,1663,1693,1723,1747,1789,1949,2053,2087,2089,2131,2251,2333,2393,2467,2549,2633,2671,2719
%N A129592 The smallest in a triple of three consecutive primes such that the ceiling of the square root of their sums-of-squares is prime.
%C A129592 Can three squares with consecutive prime sides prime(i), i=k,...,k+2, be contained/morphed in a larger square also with prime sides just slightly greater than required?
%C A129592 The areas are the squares of the prime sides; the total area is their sum prime(k)^2 + prime(k+1)^2 + prime(k+2)^2, and pulling the square root is the diagonal of the hosting square. The sequence lists the first, prime(k), if this diagonal (rounded up) is a prime number, indicating that a rather tight enclosing square with (again) a prime side length can be found.
%F A129592 {A000040(n): ceiling(sqrt(A133529(n))) in A000040}. - _R. J. Mathar_, Jul 10 2011
%e A129592 Take 13,17,19 with summed squares 169 + 289 + 361 = 819 = A133529(6). The square root is approximately 28.6 and rounding up to 29 yields a prime, so 13 is a term.
%t A129592 Select[Partition[Prime[Range[400]],3,1],PrimeQ[Ceiling[ Sqrt[ Total[ #^2]]]]&][[All,1]] (* _Harvey P. Dale_, Feb 05 2019 *)
%K A129592 nonn
%O A129592 1,1
%A A129592 _J. M. Bergot_, May 30 2007
%E A129592 Edited and extended by _R. J. Mathar_, Jul 10 2011