%I A161533
%S A161533 623071,779377,1744891,2055853,2906887,3168721,3540793,4177573,4245643,
%T A161533 4245679,4309957,4449127,4833271,4858981,5541187,5550583,5710531,5710567,
%U A161533 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 By definition, the two gaps p2-p1, p3-p2 and the double gap p3-p1 form 
               a Pythagorean triple.
%C A161533 Gap pairs p1-p2, p3-p2 occur as 36,64, or 64,36 at least through a(n) 
               <= 10^8.
%e A161533 623071 is the smallest of the consecutive primes 623071, 623107, and 
               623171 with gaps 623107-623071=36,
%e A161533 623171-623107=64, and the double gap 623171-623071= 100 each a perfect 
               square.
%Y A161533 Cf. A161002, A138198
%Y A161533 Sequence in context: A106780 A156866 A122131 this_sequence A053877 A141815 
               A048924
%Y A161533 Adjacent sequences: A161530 A161531 A161532 this_sequence A161534 A161535 
               A161536
%K A161533 nonn
%O A161533 1,1
%A A161533 Ki Punches (ki1212(AT)pocketmail.com), Jun 13 2009
%E A161533 5710567 inserted by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 
               23 2009