|
| |
|
|
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; 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
| J. Brennan, 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: A124261 A077755 A018883 * A061268 A122604 A024780
Adjacent sequences: A066727 A066728 A066729 * A066731 A066732 A066733
|
|
|
KEYWORD
| more,nonn
|
|
|
AUTHOR
| Phil Carmody (pc+oeis(AT)asdf.org), Jan 15 2002
|
| |
|
|
