55] ON THE CALCULATION OF BERNOULLI'S NUMBERS. 455 



It readily follows from Staudt's theorem that if the fractional part of 



the nth number of Bernoulli be converted into a repeating decimal, then 

 the number of figures in the repeating part will be either 2n or a divisor 



of 2n, and the first figure of the repeating part will occupy the second place 

 of decimals. 



Table of Bernoulli's Numbers expressed in Integers and Repeating Decimals. 



No. No. 



1 -16 i 



2 'OS 2 



3 -02380 95 3 



4 '03 4 



5 -075 5 



6 -25311 35 6 



7 1 -16 7 



8 7 -09215 68627 45098 03 8 



9 54 -97117 79448 62155 3884 9 



10 529 -124 10 



11 6192 -12318 84057 97101 44927 536 n 



12 86580 -25311 35 12 



13 14 25517 -16 13 



14 272 98231 '06781 60919 54022 98850 57471 2643 14 



15 6015 80873 '90064 23683 84303 86817 48359 16771 4 15 



16 1 51163 15767 '09215 68627 45098 03 16 



17 42 96146 43061 '16 17 



18 1371 16552 05088 '33277 21590 87948 5616 18 



19 48833 23189 73593 '16 19 



20 19 29657 93419 40068 '14863 26681 4 20 



21 841 69304 75736 82615 '00055 37098 56035 43743 07862 67995 21 



57032 11517 165 



22 40338 07185 40594 55413 '07681 15942 02898 55072 463 22 



23 21 15074 86380 81991 60560 "14539 00709 21985 81560 28368 23 



79432 62411 34751 77304 96 



24 1208 66265 22296 52593 46027 '3U93 70825 25317 81943 54664 24 



94290 02370 17884 07670 7606 



25 75008 66746 07696 43668 55720 '075 25 



26 50 38778 10148 1068^ 14137 89303 '05220 12578 6163 26 



27 3652 87764 84818 12333 51104 30842 '97117 79448 62155 3884" 27 



28 2 84987 69302 45088 22262 69146 43291 '06781 60919 54022 28 



98850 57471 2643 



