%I
%S 2,3,12,21,60,184,280,364,1456,3124,5236,17185,25249,49504,233776,
%T 364144,775369,3864169,8794864
%N Numbers with everincreasing minimalsquaredeniers.
%C The Jacobi of modular reductions of a number is often used by a bignum library to give a quick (negative) answer to the question of whether an integer is an exact square. This sequence gives the cutoffs for everincreasing numbers of required modular tests, on the assumption that one is avoiding a brute force squareroot/square/compare. All terms to 8794864 found by Jack Brennen.
%H J. Brennen, discussion about <a href="http://groups.yahoo.com/group/primenumbers/message/4801">issquare() tests without use of sqrt()</a> on Caldwell's 'primenumbers' list
%e 2 is 'squaredenied' by 3, as 2 is not a quadratic residue mod 3 3 is squaredenied by 2^2=4, but not by any lower prime power (2 or 3) 12 has 5 as its minimal squaredenier (0 mod 2, 0 mod 3, 0 mod 4 all QRs) 21 has 2^3=8 as its minimal squaredenier. (note that 24 has 7 as its minimal squaredenier, the first number with that property, but it is larger than 21)
%K more,nonn
%O 0,1
%A _Phil Carmody_, Jan 15 2002
