cyclic numbers造句

• For a necessary and sufficient condition, see cyclic number.
• Allowing leading zeros, the sequence of cyclic numbers begins:
• See also the article 142857 for more properties of this cyclic number.
• Confusingly, Sloane's OEIS refers to these primes as " cyclic numbers ."
• These specific integers, known as "'transposable integers "', can be but are not always cyclic numbers.
• If leading zeros are not permitted on numerals, then 142857 is the only cyclic number in decimal, due to the necessary structure given in the next section.
• Not all values of " p " will yield a cyclic number using this formula; for example " p " = 13 gives 076923 076923.
• Thus, whether dividing one by two for perfect square ( 4 2 ), fractions expressed in hexadecimal have an odd period much more often than decimal ones, and there are no cyclic numbers ( other than trivial single digits ).
• Therefore the digital expansion of 1 / p in base " b " repeats the digits of the corresponding cyclic number infinitely, as does that of a / p with rotation of the digits for any " a " between 1 and " p "  " 1.
• Using the above technique, cyclic numbers can be found in other numeric bases . ( Note that not all of these follow the second rule ( all successive multiples being cyclic permutations ) listed in the Special Cases section above ) In each of these cases the digits across half the period add up to the base minus one.
• Since it is now certain that every possible combination of the three cyclic numbers finds its place in the Julian Period, it is evident that the first year of the Christian era, which was the 10th year of a Solar Cycle, the 2nd of a Lunar Cycle, and the 4th of a Cycle of Indiction, finds its place within this artificial era, and must answer to that particular year of the period which is characterized by the same cyclic numbers.
• Since it is now certain that every possible combination of the three cyclic numbers finds its place in the Julian Period, it is evident that the first year of the Christian era, which was the 10th year of a Solar Cycle, the 2nd of a Lunar Cycle, and the 4th of a Cycle of Indiction, finds its place within this artificial era, and must answer to that particular year of the period which is characterized by the same cyclic numbers.