%I A070258
%S A070258 48,98,124,242,243,342,350,423,475,548,603,724,774,844,845,846,1024,
%T A070258 1250,1274,1323,1375,1420,1448,1519,1664,1674,1680,1681,1682,1848,1862,
%U A070258 1924,2007,2023,2056,2106,2150,2223,2275,2348,2366,2523,2527,2574,2644
%N A070258 Smallest of 3 consecutive numbers each divisible by a square.
%C A070258 The sequence includes an infinite family of arithmetic progressions. 
               Such AP's can be constructed to each term, with large differences 
               [like e.g. square of primorials, A061742]. It is necessary to solve 
               suitable systems of linear Diophantine equations. E.g.: subsequences 
               of triples of terms = {900a+548, 900a+549, 900a+550}=4(225f+137), 
               9(100f+61), 25(36f+22)}; starting terms in this sequence ={549, 1458, 
               2358, ...}; difference = A002110(3)^2. - Labos E. (labos(AT)ana.sote.hu), 
               Nov 25 2002
%D A070258 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 48, p. 18, Ellipses, 
               Paris 2008.
%t A070258 f[n_] := Union[ Transpose[ FactorInteger[n]] [[2]]] [[ -1]]; a = 0; b 
               = 1; Do[c = f[n]; If[a> 1 && b > 1 && c > 1, Print[n - 2]]; a = b; 
               b = c, {n, 3, 10^6}]
%Y A070258 Cf. A068781.
%Y A070258 Sequence in context: A031486 A044186 A044567 this_sequence A113797 A044235 
               A044616
%Y A070258 Adjacent sequences: A070255 A070256 A070257 this_sequence A070259 A070260 
               A070261
%K A070258 nonn
%O A070258 0,1
%A A070258 Sharon Sela (sharonsela(AT)hotmail.com), May 09 2002
%E A070258 More terms from Jason Earls (zevi_35711(AT)yahoo.com) and Robert G. Wilson 
               v (rgwv(AT)rgwv.com), May 10 2002