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A066730 Numbers with ever-increasing minimal-square-deniers. 1
2, 3, 12, 21, 60, 184, 280, 364, 1456, 3124, 5236, 17185, 25249, 49504, 233776, 364144, 775369, 3864169, 8794864 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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 ever-increasing numbers of required modular tests, on the assumption that one is avoiding a brute force square-root/square/compare. All terms to 8794864 found by Jack Brennen.

LINKS

Table of n, a(n) for n=0..18.

J. Brennen, discussion about issquare() tests without use of sqrt() on Caldwell's 'primenumbers' list

EXAMPLE

2 is 'square-denied' by 3, as 2 is not a quadratic residue mod 3 3 is square-denied by 2^2=4, but not by any lower prime power (2 or 3) 12 has 5 as its minimal square-denier (0 mod 2, 0 mod 3, 0 mod 4 all QRs) 21 has 2^3=8 as its minimal square-denier. (note that 24 has 7 as its minimal square-denier, the first number with that property, but it is larger than 21)

CROSSREFS

Sequence in context: A096632 A124261 A018883 * A077755 A061268 A122604

Adjacent sequences:  A066727 A066728 A066729 * A066731 A066732 A066733

KEYWORD

more,nonn

AUTHOR

Phil Carmody, Jan 15 2002

STATUS

approved

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Last modified May 26 02:35 EDT 2019. Contains 323579 sequences. (Running on oeis4.)