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A070258 Smallest of 3 consecutive numbers each divisible by a square. 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

FORMULA

a(n) = A235578(n) - 1. - Amiram Eldar, Feb 09 2021

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. A002110, A013929, A061742, A068781, A235578.

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 and Robert G. Wilson v, May 10 2002

Offset corrected by Amiram Eldar, Feb 09 2021

STATUS

approved

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Last modified October 23 21:27 EDT 2021. Contains 348217 sequences. (Running on oeis4.)