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 A161533 #17 Mar 31 2023 19:27:00
%S A161533 623071,779377,1744891,2055853,2906887,3168721,3540793,4177573,
%T A161533 4245643,4245679,4309957,4449127,4833271,4858981,5541187,5550583,
%U A161533 5710531,5710567,5856931,6013591,6789637,6855493,7024627,7162339,7340383,7614847,8143501
%N A161533 The smallest of three consecutive primes p1 < p2 < p3, where p2-p1, p3-p2, and p3-p1 are all perfect squares.
%C A161533 Note that sqrt(p2-p1), sqrt(p3-p2), sqrt(p3-p1) form a Pythagorean triple. [corrected by _James R. Buddenhagen_, Jul 09 2013]
%C A161533 Gap pairs p1-p2, p3-p2 occur as 36,64, or 64,36 at least through a(n) <= 10^8.
%H A161533 T. D. Noe, <a href="/A161533/b161533.txt">Table of n, a(n) for n = 1..1000</a>
%e A161533 623071 is the smallest of the consecutive primes 623071, 623107, and 623171 with gaps 623107-623071 = 36, 623171-623107 = 64, and the double gap 623171-623071 = 100 each a perfect square.
%t A161533 PerfectSquareQ[n_] := JacobiSymbol[n, 13] =!= -1 && JacobiSymbol[n, 19] =!= -1 && JacobiSymbol[n, 17] =!= -1 && JacobiSymbol[n, 23] =!= -1 && IntegerQ[Sqrt[n]]; t = {}; n = 2; p1 = 1; p2 = 2; p3 = 3; While[Length[t] < 30, n++; p1 = p2; p2 = p3; p3 = Prime[n]; If[PerfectSquareQ[p2 - p1] && PerfectSquareQ[p3 - p2] && PerfectSquareQ[p3 - p1], AppendTo[t, p1]]]; t (* _T. D. Noe_, Jul 09 2013 *)
%t A161533 psQ[{a_,b_,c_}]:=AllTrue[{Sqrt[b-a],Sqrt[c-b],Sqrt[c-a]},IntegerQ]; Transpose[ Select[Partition[ Prime[Range[600000]],3,1],psQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 20 2014 *)
%Y A161533 Cf. A161002, A138198.
%K A161533 nonn
%O A161533 1,1
%A A161533 _Ki Punches_, Jun 13 2009
%E A161533 5710567 inserted by _R. J. Mathar_, Sep 23 2009