

A070258


Smallest of 3 consecutive numbers each divisible by a square.


12



48, 98, 124, 242, 243, 342, 350, 423, 475, 548, 603, 724, 774, 844, 845, 846, 1024, 1250, 1274, 1323, 1375, 1420, 1448, 1519, 1664, 1674, 1680, 1681, 1682, 1848, 1862, 1924, 2007, 2023, 2056, 2106, 2150, 2223, 2275, 2348, 2366, 2523, 2527, 2574, 2644
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OFFSET

0,1


COMMENTS

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


REFERENCES

J.M. De Koninck, Ces nombres qui nous fascinent, Entry 48, p. 18, Ellipses, Paris 2008.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000


MATHEMATICA

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}]
Flatten[Position[Partition[SquareFreeQ/@Range[3000], 3, 1], _?(Union[#] == {False}&), {1}, Heads>False]] (* Harvey P. Dale, May 24 2014 *)


CROSSREFS

Cf. A068781.
Sequence in context: A031486 A044186 A044567 * A260248 A260001 A260241
Adjacent sequences: A070255 A070256 A070257 * A070259 A070260 A070261


KEYWORD

nonn


AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), May 09 2002


EXTENSIONS

More terms from Jason Earls (zevi_35711(AT)yahoo.com) and Robert G. Wilson v, May 10 2002


STATUS

approved



