Mixing
士的數
第n個士的數（cabtaxi number），表示為Cabtaxi(n)，定義為能以n種方法寫成兩個或正或負或零的立方數之和的正整數中最小者。它的名字來自的士數的顛倒。對任何的n，這樣的數均存在，因為的士數對所有的n都存在。現時只有10個士的數是已知的
A047696：
- Cabtaxi(1)=1=13±03{displaystyle {begin{matrix}mathrm {Cabtaxi} (1)&=&1&=&1^{3}pm 0^{3}end{matrix}}}
- Cabtaxi(2)=91=33+43=63−53{displaystyle {begin{matrix}mathrm {Cabtaxi} (2)&=&91&=&3^{3}+4^{3}\&&&=&6^{3}-5^{3}end{matrix}}}
- Cabtaxi(3)=728=63+83=93−13=123−103{displaystyle {begin{matrix}mathrm {Cabtaxi} (3)&=&728&=&6^{3}+8^{3}\&&&=&9^{3}-1^{3}\&&&=&12^{3}-10^{3}end{matrix}}}
- Cabtaxi(4)=2741256=1083+1143=1403−143=1683−1263=2073−1833{displaystyle {begin{matrix}mathrm {Cabtaxi} (4)&=&2741256&=&108^{3}+114^{3}\&&&=&140^{3}-14^{3}\&&&=&168^{3}-126^{3}\&&&=&207^{3}-183^{3}end{matrix}}}
- Cabtaxi(5)=6017193=1663+1133=1803+573=1853−683=2093−1463=2463−2073{displaystyle {begin{matrix}mathrm {Cabtaxi} (5)&=&6017193&=&166^{3}+113^{3}\&&&=&180^{3}+57^{3}\&&&=&185^{3}-68^{3}\&&&=&209^{3}-146^{3}\&&&=&246^{3}-207^{3}end{matrix}}}
- Cabtaxi(6)=1412774811=9633+8043=11343−3573=11553−5043=12463−8053=21153−20043=47463−47253{displaystyle {begin{matrix}mathrm {Cabtaxi} (6)&=&1412774811&=&963^{3}+804^{3}\&&&=&1134^{3}-357^{3}\&&&=&1155^{3}-504^{3}\&&&=&1246^{3}-805^{3}\&&&=&2115^{3}-2004^{3}\&&&=&4746^{3}-4725^{3}end{matrix}}}
- Cabtaxi(7)=11302198488=19263+16083=19393+15893=22683−7143=23103−10083=24923−16103=42303−40083=94923−94503{displaystyle {begin{matrix}mathrm {Cabtaxi} (7)&=&11302198488&=&1926^{3}+1608^{3}\&&&=&1939^{3}+1589^{3}\&&&=&2268^{3}-714^{3}\&&&=&2310^{3}-1008^{3}\&&&=&2492^{3}-1610^{3}\&&&=&4230^{3}-4008^{3}\&&&=&9492^{3}-9450^{3}end{matrix}}}
- Cabtaxi(8)=137513849003496=229443+500583=365473+445973=369843+442983=521643−164223=531303−231843=573163−370303=972903−921843=2183163−2173503{displaystyle {begin{matrix}mathrm {Cabtaxi} (8)&=&137513849003496&=&22944^{3}+50058^{3}\&&&=&36547^{3}+44597^{3}\&&&=&36984^{3}+44298^{3}\&&&=&52164^{3}-16422^{3}\&&&=&53130^{3}-23184^{3}\&&&=&57316^{3}-37030^{3}\&&&=&97290^{3}-92184^{3}\&&&=&218316^{3}-217350^{3}end{matrix}}}
- Cabtaxi(9)=424910390480793000=6452103+5386803=6495653+5323153=7524093−1014093=7597803−2391903=7738503−3376803=8348203−5393503=14170503−13426803=31798203−31657503=59600103−59560203{displaystyle {begin{matrix}mathrm {Cabtaxi} (9)&=&424910390480793000&=&645210^{3}+538680^{3}\&&&=&649565^{3}+532315^{3}\&&&=&752409^{3}-101409^{3}\&&&=&759780^{3}-239190^{3}\&&&=&773850^{3}-337680^{3}\&&&=&834820^{3}-539350^{3}\&&&=&1417050^{3}-1342680^{3}\&&&=&3179820^{3}-3165750^{3}\&&&=&5960010^{3}-5956020^{3}end{matrix}}}
- Cabtaxi(10)=933528127886302221000=774801303−774282603=413376603−411547503=184216503−174548403=108526603−70115503=100600503−43898403=98771403−31094703=97813173−13183173=97733303−845603=84443453+69200953=83877303+70028403{displaystyle {begin{matrix}mathrm {Cabtaxi} (10)&=&933528127886302221000&=&77480130^{3}-77428260^{3}\&&&=&41337660^{3}-41154750^{3}\&&&=&18421650^{3}-17454840^{3}\&&&=&10852660^{3}-7011550^{3}\&&&=&10060050^{3}-4389840^{3}\&&&=&9877140^{3}-3109470^{3}\&&&=&9781317^{3}-1318317^{3}\&&&=&9773330^{3}-84560^{3}\&&&=&8444345^{3}+6920095^{3}\&&&=&8387730^{3}+7002840^{3}end{matrix}}}
在Cabtaxi(3){displaystyle mathrm {Cabtaxi} (3)}
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