Peggy Sue’s Fraction:
Peggy Sue is a sweet Italian girl who has a
thing about the number 13. She found
that the number 76,923,076,922,923,076,923,077 has an interesting property that
relates to the number 13. It is
divisible by 13, but that’s not the amazing thing. If you take the inverse of this number and
convert it to a decimal expansion you get the 13 times table, starting with 0 *
13, and written in 12 digit chunks.
1 / 76,923,076,922,923,076,923,077 =
0.
000000000000 000000000013 000000000026 000000000039
000000000052 000000000065 000000000078 000000000091
000000000104 000000000117 000000000130 000000000143
000000000156 000000000169 000000000182 000000000195
000000000208 000000000221 000000000234 000000000247
000000000260 000000000273 000000000286 000000000299
000000000312 000000000325 000000000338 000000000351
000000000364 000000000377 000000000390 000000000403
000000000416 000000000429 000000000442 000000000455
000000000468 000000000481 000000000494 000000000507
000000000520 000000000533 000000000546 000000000559
000000000572 000000000585 000000000598 000000000611
000000000624 000000000637 000000000650 000000000663
000000000676 000000000689 000000000702 000000000715
000000000728 000000000741 000000000754 000000000767
000000000780 000000000793 000000000806 000000000819
000000000832 000000000845 000000000858 000000000871
000000000884 000000000897 000000000910 000000000923
000000000936 000000000949 000000000962 000000000975
000000000988 000000001001 000000001014 000000001027
000000001040 000000001053 000000001066 000000001079
000000001092 000000001105 000000001118 000000001131
000000001144 000000001157 000000001170 000000001183
000000001196 000000001209 000000001222 000000001235
000000001248 000000001261 000000001274 000000001287
000000001300 000000001313 000000001326 000000001339
000000001352 000000001365 000000001378 000000001391
000000001404 000000001417 000000001430 000000001443
000000001456 000000001469 000000001482 000000001495
000000001508 000000001521 000000001534 000000001547
000000001560 000000001573 000000001586 000000001599
000000001612 000000001625 000000001638 000000001651
000000001664 000000001677 000000001690 000000001703
000000001716 000000001729 000000001742 000000001755
000000001768 000000001781 000000001794 000000001807
000000001820 000000001833 000000001846 000000001859
000000001872 000000001885 000000001898 000000001911
000000001924 000000001937 000000001950 000000001963
000000001976 000000001989 000000002002 000000002015
000000002028 000000002041 000000002054 000000002067
000000002080 000000002093 000000002106 000000002119
000000002132 000000002145 000000002158 000000002171
000000002184 000000002197 000000002210 000000002223
000000002236 000000002249 000000002262 000000002275
000000002288 000000002301 000000002314 000000002327
000000002340 000000002353 000000002366 000000002379
000000002392 000000002405 000000002418 000000002431
000000002444 000000002457 000000002470 000000002483
000000002496 000000002509 000000002522 000000002535
000000002548 000000002561 000000002574 000000002587
000000002600 000000002613 000000002626 000000002639
000000002652 000000002665 000000002678 000000002691
000000002704 000000002717 000000002730 000000002743
000000002756 000000002769 000000002782 000000002795
000000002808 000000002821 000000002834 000000002847
000000002860 000000002873 000000002886 000000002899
000000002912 000000002925 000000002938 000000002951
000000002964 000000002977 000000002990 000000003003
000000003016 000000003029 000000003042 000000003055
000000003068 000000003081 000000003094 000000003107
000000003120 000000003133 000000003146 000000003159
000000003172 000000003185 000000003198 000000003211
000000003224 000000003237 000000003250 000000003263
000000003276 000000003289 000000003302 000000003315
000000003328 000000003341 000000003354 000000003367
000000003380 000000003393 000000003406 000000003419
000000003432 000000003445 000000003458 000000003471
000000003484 000000003497 000000003510 000000003523
000000003536 000000003549 000000003562 000000003575
000000003588 000000003601 000000003614 000000003627
000000003640 000000003653 000000003666 000000003679
000000003692 000000003705 000000003718 000000003731
000000003744 000000003757 000000003770 000000003783
000000003796 000000003809 000000003822 000000003835
000000003848 000000003861 000000003874 000000003887
000000003900 000000003913 000000003926 000000003939
000000003952 000000003965 000000003978 000000003991
000000004004 000000004017 000000004030 000000004043
000000004056 000000004069 000000004082 000000004095
000000004108 000000004121 000000004134 000000004147
000000004160 000000004173 000000004186 000000004199
000000004212 000000004225 ...
000000000000 000000000013 000000000026 000000000039
000000000052 000000000065 000000000078 000000000091
000000000104 000000000117 000000000130 000000000143
000000000156 000000000169 000000000182 000000000195
000000000208 000000000221 000000000234 000000000247
000000000260 000000000273 000000000286 000000000299
000000000312 000000000325 000000000338 000000000351
000000000364 000000000377 000000000390 000000000403
000000000416 000000000429 000000000442 000000000455
000000000468 000000000481 000000000494 000000000507
000000000520 000000000533 000000000546 000000000559
000000000572 000000000585 000000000598 000000000611
000000000624 000000000637 000000000650 000000000663
000000000676 000000000689 000000000702 000000000715
000000000728 000000000741 000000000754 000000000767
000000000780 000000000793 000000000806 000000000819
000000000832 000000000845 000000000858 000000000871
000000000884 000000000897 000000000910 000000000923
000000000936 000000000949 000000000962 000000000975
000000000988 000000001001 000000001014 000000001027
000000001040 000000001053 000000001066 000000001079
000000001092 000000001105 000000001118 000000001131
000000001144 000000001157 000000001170 000000001183
000000001196 000000001209 000000001222 000000001235
000000001248 000000001261 000000001274 000000001287
000000001300 000000001313 000000001326 000000001339
000000001352 000000001365 000000001378 000000001391
000000001404 000000001417 000000001430 000000001443
000000001456 000000001469 000000001482 000000001495
000000001508 000000001521 000000001534 000000001547
000000001560 000000001573 000000001586 000000001599
000000001612 000000001625 000000001638 000000001651
000000001664 000000001677 000000001690 000000001703
000000001716 000000001729 000000001742 000000001755
000000001768 000000001781 000000001794 000000001807
000000001820 000000001833 000000001846 000000001859
000000001872 000000001885 000000001898 000000001911
000000001924 000000001937 000000001950 000000001963
000000001976 000000001989 000000002002 000000002015
000000002028 000000002041 000000002054 000000002067
000000002080 000000002093 000000002106 000000002119
000000002132 000000002145 000000002158 000000002171
000000002184 000000002197 000000002210 000000002223
000000002236 000000002249 000000002262 000000002275
000000002288 000000002301 000000002314 000000002327
000000002340 000000002353 000000002366 000000002379
000000002392 000000002405 000000002418 000000002431
000000002444 000000002457 000000002470 000000002483
000000002496 000000002509 000000002522 000000002535
000000002548 000000002561 000000002574 000000002587
000000002600 000000002613 000000002626 000000002639
000000002652 000000002665 000000002678 000000002691
000000002704 000000002717 000000002730 000000002743
000000002756 000000002769 000000002782 000000002795
000000002808 000000002821 000000002834 000000002847
000000002860 000000002873 000000002886 000000002899
000000002912 000000002925 000000002938 000000002951
000000002964 000000002977 000000002990 000000003003
000000003016 000000003029 000000003042 000000003055
000000003068 000000003081 000000003094 000000003107
000000003120 000000003133 000000003146 000000003159
000000003172 000000003185 000000003198 000000003211
000000003224 000000003237 000000003250 000000003263
000000003276 000000003289 000000003302 000000003315
000000003328 000000003341 000000003354 000000003367
000000003380 000000003393 000000003406 000000003419
000000003432 000000003445 000000003458 000000003471
000000003484 000000003497 000000003510 000000003523
000000003536 000000003549 000000003562 000000003575
000000003588 000000003601 000000003614 000000003627
000000003640 000000003653 000000003666 000000003679
000000003692 000000003705 000000003718 000000003731
000000003744 000000003757 000000003770 000000003783
000000003796 000000003809 000000003822 000000003835
000000003848 000000003861 000000003874 000000003887
000000003900 000000003913 000000003926 000000003939
000000003952 000000003965 000000003978 000000003991
000000004004 000000004017 000000004030 000000004043
000000004056 000000004069 000000004082 000000004095
000000004108 000000004121 000000004134 000000004147
000000004160 000000004173 000000004186 000000004199
000000004212 000000004225 ...
How long does this pattern continue? I don’t know yet. It takes time to do long division.
Back to Fibonacci review tomorrow.
David
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