3Xn+1)/2^m=1 鈥冣€�3Xn+1)2^m=1
鈥冣€冧粠鍥句功棣嗗嚭鏉ワ紝闄堣垷鍜屾潹渚濅緷璧板湪鍥炲�鑸嶇殑璺�笂銆�
鈥冣€冧袱浜鸿蛋鍒版棤鍚嶆箹鏃讹紝涓嶈嚜瑙夌殑閮藉仠浜嗕笅鏉ャ€�
鈥冣€冨湪鐏�厜鐨勭収鑰€涓嬶紝鏃犲悕婀栧埆鏈変竴鐣�櫙鑹层€�
鈥冣€冮檲鑸熷亸澶寸湅鐫€鏉ㄤ緷渚濓紝杞诲０璇撮亾锛氣€滀緷渚濓紝鎴戜滑娌跨潃鏃犲悕婀栬蛋浼氬惂锛熲€�
鈥冣€冩潹渚濅緷鐐圭偣澶达細鈥滃ソ銆傗€�
鈥冣€冮檲鑸熺壍璧锋潹渚濅緷鐨勬墜锛屼袱涓�汉灏辫繖鏍烽潤闈欒蛋鍦ㄦ棤鍚嶆箹鐣斻€�
鈥冣€冨�瑙傛潵璇达紝鐕曞ぇ涓嶄粎浠呮槸鍗庡浗鐨勯《灏栧悕鏍★紝鍏舵牎鍥�櫙鑹蹭篃鍙�互绉板緱涓婃槸鍗庡浗鏈€缇庡ぇ瀛︿箣涓€銆�
鈥冣€冩瘯绔燂紝鐕曞ぇ鏍″洯閲屾湁鐫€涓嶅皯鍙よ壊鍙ら�鐨勫缓绛戯紝鑰屼笖瀹冧滑杩樺叿鏈変竴瀹氱殑鍘嗗彶鎰忎箟銆�
鈥冣€冨氨鎷跨嚂鍥�潵璇达紝鏈€鏃╂槸鏄庢湞鏃舵湡鐨勫嫼鍥�紝鍚庢潵鏄�竻鏈濈殑鐨囧�鍥�灄銆�
鈥冣€冪幇濡備粖鎴愪负浜嗙嚂澶ф牎鍥�€�
鈥冣€冭€岀嚂澶ф渶钁楀悕鐨勶紝渚挎槸闄堣垷涓や汉姝ゅ埢姝ｉ棽閫涚潃鐨勬棤鍚嶆箹浜嗐€�
鈥冣€冨畠涓庨泤鍗氬�銆佺嚂澶у浘涔﹂�骞剁О涓衡€滀竴濉旀箹鍥锯€濄€�
鈥冣€冨�鏋滅瓑鍒拌幉鑺辩洓寮€锛屾棤鍚嶆箹杈规暣涓�兘鏄�竻棣欏洓婧€€�
鈥冣€冨啀鍔犱笂宀歌竟鐨勯泤鍗氬�锛岄珮鑰稿叆浜戯紝宸嶇劧灞圭珛锛屼豢浣涢晣瀹堝北姘翠竴鑸�€�
鈥冣€冩棤鍚嶆箹鐨勫姩锛屾惌閰嶄笂闆呭崥濉旂殑闈欙紝婀栧姩濉旈潤锛屾箹鏌斿�鍧氾紝濉斾笌婀栫浉寰楃泭褰般€�
鈥冣€冮檲鑸熸寚鐫€杩滃�鐨勯泤鍗氬�锛岃交澹伴棶閬擄細鈥滀緷渚濓紝浣犵煡閬撹繖闆呭崥濉斿師鍏堟槸鍋氫粈涔堢殑鍚楋紵鈥�
鈥冣€冩潹渚濅緷鐪嬩簡涓€鐪煎�瑙備豢鍒剁噧鐏�彜濉旂殑闆呭崥濉旓紝绗戠潃璇撮亾锛氣€滄垜褰撶劧鐭ラ亾浜嗭紝瀹冩渶鍒濇槸浣滀负渚涙按姘村�浣跨敤鐨勩€傗€�
鈥冣€冮檲鑸熻交杞荤偣澶达紝鍙堥棶閬擄細鈥滈偅浣犵煡閬撻泤鍗氬�鍜屾棤鍚嶆箹鐨勫瘬鎰忓悧锛熲€�
鈥冣€冩潹渚濅緷鎯充簡鎯筹紝鍥為亾锛氣€滈泤鍗氬�瀵撴剰鍗氶泤锛屾棤鍚嶆箹鐨勮瘽锛屾垜灏变笉鐭ラ亾浜嗐€傗€�
鈥冣€冮檲鑸熷仠涓嬭剼姝ワ紝鏈涘悜杩滃�鐨勯泤鍗氬�锛岀紦缂撹�閬擄細鈥滈泤鍗氬�鍓嶆眰鍗氶泤锛屾棤鍚嶆箹鐣旇獡闂诲悕銆傚畠浠�殑瀵撴剰灏辨槸锛屽湪鏃犲悕婀栧彂瑾擄紝鎴愪负涓€鍚嶅崥闆呬箣浜恒€傗€�
鈥冣€冩潹渚濅緷绗戠湅鐫€闄堣垷锛氣€滃ソ鍟﹀ソ鍟︼紝鐭ラ亾浣犳槸璇�枃瀛﹂湼銆傗€�
鈥冣€冣€滃樋鍢裤€傗€濋檲鑸熶笉濂芥剰鎬濈殑绗戜簡绗戙€�
鈥冣€冩潹渚濅緷鐪嬩簡闄堣垷涓€鐪硷紝杞诲０闂�亾锛氣€滀綘鏄�笉鏄�湁浠€涔堝績浜嬶紵鈥�
鈥冣€冮檲鑸熸憞浜嗘憞澶达紝鍙堢偣浜嗙偣澶达紝鍗存病鏈夎�璇濄€�
鈥冣€冭�姝わ紝鏉ㄤ緷渚濇煍澹伴亾锛氣€滆�棰樼殑浜嬶紵鈥�
鈥冣€冣€滃棷銆傗€濋檲鑸熺偣鐐瑰ご锛屸€滀粖澶╁皬鐝��锛屽紶鏁欐巿璁蹭簡涓€涓�暟瀛︽父鎴忥紝绠楁槸鍚�彂鎬х殑涓€鑺傝�鍚с€傗€�
鈥冣€冩潹渚濅緷闂�亾锛氣€滀粈涔堟父鎴忥紵鈥�
鈥冣€冮檲鑸燂細鈥滃啺闆圭寽鎯炽€傗€�
鈥冣€冭仾鎱у�鏉ㄤ緷渚濓紝鑷�劧鏄庣櫧浜嗛檲鑸熺殑鎰忔€濄€�
鈥冣€冨ス鎯充簡鎯筹紝璇撮亾锛氣€滄妸杩欎釜浣滀负璇鹃�鐮旂┒锛岀‘瀹炴湁浜涢毦浜嗐€備絾鏄�綘閮藉喅瀹氬ソ浜嗙殑璇濓紝鍙堜负浠€涔堢姽璞�憿锛熲€�
鈥冣€冮檲鑸熸壄澶寸湅鐫€鏉ㄤ緷渚濓紝浠栫‘瀹炴槸鐘硅鲍浜嗐€�
鈥冣€冭櫧鐒跺仛鍑轰簡鐮旂┒鍐伴浌鐚滄兂鐨勫喅瀹氾紝涔熺粰鑷�繁璁剧疆浜嗕竴涓�湡闄愩€�
鈥冣€冧絾鏄�紝杩欑�涓栫晫鎬х殑闅鹃�锛屼粬杩樻槸鏈変簺鍙戞喎銆�
鈥冣€冩渶鎬曡姳璐逛簡鏃堕棿锛屽嵈浠€涔堜篃娌″緱鍒般€�
鈥冣€冮檲鑸熷潶瑷€閬擄細鈥滄垜涓嶇煡閬撹兘涓嶈兘瀹屾垚杩欎釜璇鹃�銆傗€�
鈥冣€冩潹渚濅緷鍙嶆墜鎻＄揣闄堣垷鐨勬墜锛屾煍澹拌�閬擄細鈥滆繖鏍风姽璞�紝灏变笉鍍忎綘浜嗗摝銆傞偅涓�暍鍜屽叏鏍″笀鐢熷仛鍑�725鐨勭害瀹氾紝鏁㈠湪澶т竴灏辫�鍒掔潃瀹屾垚鏁板�绯诲拰鐗╃悊绯诲弻姣曚笟鐨勪汉锛屽簲璇ユ槸涓€涓�亣鍒颁换浣曚簨锛岄兘涓嶄細鐘硅鲍鐨勪汉銆傗€�
鈥冣€冣€滄垜浠�兘涓嶇煡閬撴湭鏉ユ槸鎬庢牱鐨勶紝浣嗘垜浠�彲浠ヤ负浜嗘湭鏉ュ幓璧板ソ浠婂ぉ鐨勬瘡涓€姝ャ€傝€岃繖涓��棰樼殑缁撴灉濡備綍锛屼篃搴旇�鏄�仛浜嗕箣鍚庯紝鎵嶄細鐭ラ亾鐨勩€傗€�
鈥冣€冣€滄渶閲嶈�鐨勬槸锛屾垜鐩镐俊浣犵殑鍐冲畾銆傗€�
鈥冣€冭繖杩樻槸闄堣垷绗�竴娆″惉鏉ㄤ緷渚濊�杩欎箞澶氾紝浠栦粠鏉ㄤ緷渚濈殑鐪肩�涓�紝鐪嬪埌鐨勬槸瀹屽叏鐨勭浉淇°€�
鈥冣€冮檲鑸熻交杞讳竴绗戯紝鐢ㄥ彟涓€鍙�墜鎻変簡鎻夋潹渚濅緷鐨勮剳琚嬶細鈥滀綘璇村緱瀵癸紝搴旇�鏄�仛浜嗘墠鐭ラ亾銆傝€屼笉鏄�湪宸茬粡鍐冲畾浜嗕箣鍚庯紝杩樼姽鐘硅鲍璞�€傗€濃€冣€冣€冣€冣€滃�鍛€銆傗€濇潹渚濅緷绗戠潃璇撮亾锛屸€滀笉灏卞儚浣犲垰鎵嶈�鐨勶紝闆呭崥濉斿墠姹傚崥闆咃紝鏃犲悕婀栫晹瑾撻椈鍚嶅槢锛屾垜浠�笉灏扁€︹€︹€�
鈥冣€冩潹渚濅緷璇濇湭璇村畬锛岄檲鑸熸墜涓婄獊鐒剁敤鍔涳紝涓€鎶婂皢濂规媺鍏ヤ簡鎬€閲屻€�
鈥冣€冧粬鎶辩殑寰堢揣銆�
鈥冣€冨ス鐨勫弻鎵嬩篃浠庝竴寮€濮嬬殑鎯婃厡澶辨帾锛岃浆鑰岀紦缂撴惌鍦ㄤ粬鐨勮韩涓娿€�
鈥冣€冮檲鑸熷湪鏉ㄤ緷渚濊€宠竟鏌斿０璇撮亾锛氣€滆阿璋�綘锛屼緷渚濓紝鏈変綘鐪熷ソ銆傗€�
鈥冣€冩潹渚濅緷铏界劧骞舵湭璇磋瘽锛屼絾濂圭殑鍢磋�涓嶈嚜瑙夌殑闇插嚭浜嗗井绗戙€�
鈥冣€冭壇涔咃紝涓や汉鎵嶅垎寮€銆�
鈥冣€冮檲鑸熺湅鐫€鏉ㄤ緷渚濋€氱孩鐨勫皬鑴革紝蹇嶄笉浣忔墦瓒ｉ亾锛氣€滀綘鏄�孩鑻规灉鍙樼殑鍚楋紵鈥�
鈥冣€冣€滃摷銆傗€濇潹渚濅緷濞囧摷涓€澹帮紝鈥滀綘鎵嶆槸绾㈣嫻鏋滃憿銆傗€�
鈥冣€冮檲鑸熷洖鍒板�鑸嶆椂锛屽凡缁忓揩11鐐逛簡锛屾瘮骞冲父浠庡浘涔﹂�鍥炴潵锛岃�鏅氫笂涓嶅皯銆�
鈥冣€冧竴杩涘�鑸嶏紝璧电惁鐞︿笁浜哄氨榻愰綈鐪嬪悜闄堣垷銆�
鈥冣€冮檲鑸熺枒鎯戠殑闂�亾锛氣€滀綘浠�繖涔堢湅鐫€鎴戝共鍢涳紵鈥�
鈥冣€冧笁浜洪綈澹拌�閬擄細鈥滄病浠€涔堬紝杩樹互涓轰綘浠婃櫄涓嶅洖鏉ヤ簡鍛€€傗€�
鈥冣€冮檲鑸熷井寰�湁浜涘按灏�細鈥滄垜涓嶅洖鏉ワ紝鎴戠潯鍝�紵鈥�
鈥冣€冭档鐞︾惁璇撮亾锛氣€滈偅灏变笉鐭ラ亾浜嗐€傗€�
鈥冣€冮】浜嗛】锛岃档鐞︾惁鏁忛攼鐨勫彂鐜颁竴鐗╋紝闅忓嵆杞诲０璇撮亾锛氣€滀綘韬�笂鏈夊ス鐨勯�姘村懗锛屾槸鎴戦蓟瀛愮姱浜嗙姜鈥︹€︹€�
鈥冣€冮檲鑸燂細鈥溾€︹€︹€�
鈥冣€冩湵鏄庣悊鍜屾潕绀煎垯鍦ㄤ竴鏃佸伔绗戙€�
鈥冣€冧笉鍐嶇悊浼氳繖涓変汉锛岄檲鑸熸嬁璧疯劯鐩嗭紝鍘绘礂婕变簡銆�
鈥冣€冣€滃崸妲解€︹€︹€�
鈥冣€冩礂婕辨椂锛岄檲鑸熸墠鍙戠幇锛岃繖涓変汉涓哄暐杩欎箞鐪嬬潃鑷�繁銆�
鈥冣€冧粬鎶辨潹渚濅緷鏃讹紝鏉ㄤ緷渚濈殑澶村彂钀戒簡涓€鏍瑰湪浠栬。鏈嶄笂銆�
鈥冣€冭繕鏄�緢鏄剧溂鐨勪綅缃�€︹€�
鈥冣€冩櫄涓婏紝韬哄湪搴婁笂鐨勯檲鑸燂紝鎯宠捣鏉ㄤ緷渚濈殑璇濓紝鍢磋�涓嶈嚜瑙夌殑甯︾潃涓€涓濈瑧鎰忋€�
鈥冣€冮檲鑸熺殑鍐呭績锛屼篃鍙樺緱鏇村姞娓存湜瑙ｅ喅鍐伴浌鐚滄兂杩欎釜璇鹃�浜嗐€�
鈥冣€冪粰鏉ㄤ緷渚濆彂浜嗕釜銆愭櫄瀹夈€戯紝闄堣垷渚跨潯鐫€浜嗐€�
鈥冣€冧箣鍚庣殑鍑犲ぉ锛岄檲鑸熶竴鏂归潰鎸夌収璁″垝锛屽�涔犵潃鐗╃悊绯荤殑鏁欐潗銆�
鈥冣€冧竴鏂归潰锛屾妸澶ф妸鐨勬椂闂寸敤鍦ㄦ煡闃呭啺闆圭寽鎯崇殑鐩稿叧璇鹃�涓娿€�
鈥冣€冨€掓槸鏈変竴涓�护浠栨剰澶栫殑鍙戠幇锛岄偅灏辨槸鍏充簬寮犱腑鍘熺殑閭ｈ妭浠ｆ暟璁ㄨ�璇俱€�
鈥冣€冭�涓婃墍璁ㄨ�鐨勫唴瀹癸紝鏈変竴浜涜�璁板湪浜嗛敊棰橀泦涓娿€�
鈥冣€冭繖涔熶粠渚ч潰楠岃瘉浜嗛偅鑺傝�锛屾墍璁ㄨ�鐨勫唴瀹规槸瀛樺湪缂洪櫡鐨勩€�
鈥冣€冭€岄偅浜涙病璁板綍鐨勶紝涔熺粰闄堣垷鎻愪緵浜嗕竴浜涜�棰樺弬鑰冦€�
鈥冣€冣€滃皢闂��鍏�紡鍖栵紝鏄�В鍐崇寽鎯冲繀椤昏�鍋氱殑銆傚叧浜庡啺闆圭寽鎯筹紝鎴栬€呰�3X+1鐚滄兂锛屼粬鐨勫叕寮忔槸涓€涓�凯浠ｅ叕寮忥紝鏈夎緭鍏ワ紝鏈夎緭鍑猴紝鏈夊弽棣堚€︹€︹€�
鈥冣€冮檲鑸熷厛鎶婂啺闆圭寽鎯宠繘琛屽叕寮忓寲锛屽啀瀵瑰叾杩涜�鐮旂┒銆�
鈥冣€冦€怷n+1=(3Xn+1)/2^m锛屽紡涓�瘡涓€涓猉閮芥槸濂囨暟锛宮=1锛�2锛�3鈥︹€︺€�
鈥冣€冦€愮洿鍒版妸3X+1涓�殑鍋舵暟2^m鏋愬嚭鎶垫秷锛屼娇寰楃瓑寮忓彸杈规槸濂囨暟涓烘�銆傚�鏋滆繖涓��鏁颁笉鏄�1锛岃€屾槸鍏跺畠濂囨暟锛屽氨缁х画杩�唬锛屼竴鐩村埌1涓烘�銆傘€�
鈥冣€冦€愪篃灏辨槸璇达紝闇€瑕佽瘉鏄庣殑鏄�(3Xn+1)/2^m=1銆�