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%I #32 Jan 18 2023 02:20:54
%S 48,98,124,242,243,342,350,423,475,548,603,724,774,844,845,846,1024,
%T 1250,1274,1323,1375,1420,1448,1519,1664,1674,1680,1681,1682,1848,
%U 1862,1924,2007,2023,2056,2106,2150,2223,2275,2348,2366,2523,2527,2574,2644
%N Smallest of 3 consecutive numbers each divisible by a square.
%C 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 Elemer_, Nov 25 2002
%C The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 2, 16, 180, 1868, 18649, 186335, 1863390, 18634236, 186340191, ... . Apparently, the asymptotic density of this sequence exists and equals 0.01863... . - _Amiram Eldar_, Jan 18 2023
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 48, p. 18, Ellipses, Paris 2008.
%H Amiram Eldar, <a href="/A070258/b070258.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F a(n) = A235578(n) - 1. - _Amiram Eldar_, Feb 09 2021
%t 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}]
%t Flatten[Position[Partition[SquareFreeQ/@Range[3000],3,1],_?(Union[#] == {False}&),{1},Heads->False]] (* _Harvey P. Dale_, May 24 2014 *)
%t f@n_ := Flatten@ Position[Partition[SquareFreeQ /@ Range@2000, n, 1], Table[False, {n}]]; f@3 (* _Hans Rudolf Widmer_, Aug 30 2022 *)
%Y Subsequence of A013929 and A068781.
%Y Cf. A002110, A061742, A235578.
%K nonn
%O 1,1
%A Sharon Sela (sharonsela(AT)hotmail.com), May 09 2002
%E More terms from _Jason Earls_ and _Robert G. Wilson v_, May 10 2002
%E Offset corrected by _Amiram Eldar_, Feb 09 2021
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