

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
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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



