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Search: id:A070284
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| A070284 |
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Lesser of 4 consecutive numbers each divisible by a square. |
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+0
4
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| 242, 844, 845, 1680, 1681, 2888, 2889, 3174, 3624, 3625, 3750, 5046, 5047, 8475, 8523, 8954, 10050, 10827, 10924, 10925, 11322, 13374, 14748, 14749, 15775, 15848, 15849, 16575, 17404, 17405, 19647, 19940, 19941, 20574, 21462
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 quadruples of terms = {44100k+29349, 44100k+29350, 44100k+29351, 44100+29352} = {9(49000k+3261, 25(1764k+1174), 49(900k+599), 4(11025k+7338)}; starting terms in this sequence = {29349, 73449, 117649...}; difference = A002110(4)^2 = 2310^2. - Labos E. (labos(AT)ana.sote.hu), Nov 25 2002
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MATHEMATICA
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f[n_] := Union[Transpose[FactorInteger[n]][[2]]][[ -1]]; a = 0; b = 1; c = 0; Do[d = f[n]; If[a > 1 && b > 1 && c > 1 && d > 1, Print[n - 3]]; a = b; b = c; c = d, {n, 4, 10^6}]
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CROSSREFS
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Cf. A070258, A068781, A045882, A049535, A077647, A078143.
Adjacent sequences: A070281 A070282 A070283 this_sequence A070285 A070286 A070287
Sequence in context: A039665 A023703 A094908 this_sequence A006601 A035748 A022153
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KEYWORD
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nonn
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), May 09 2002
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 09 2002
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