呵呵
mathe也没确定11的2，3，7因子数不存在啊
如果能搜索10000位内的组合
我想得到一组的概率不会很小的
当然也有很大可能没有
我编了些程序，
得到 2^p*3^q*7^s 系列的整数，步数不小于 3 的有 587 组。
得到 3^q*5^s*7^r 系列的整数，步数不小于 3 的仅有 12 组：
No.stepsr(2,3,5,7)value14( 0, 2, 2, 1 )157524( 0, 1, 5, 2 )5953534( 0, 2, 2, 3 )7717543( 0, 2, 1, 0 )7553( 0, 2, 0, 1 )17563( 0, 1, 0, 3 )171573( 0, 3, 3, 0 )337583( 0, 5, 1, 0 )937593( 0, 4, 2, 1 )39375103( 0, 3, 7, 2 )13395375113( 0, 8, 6, 1 )1993359375123( 0, 1, 18, 1 )13559717115
以下是整理并排序后的数据（第一优先级是 steps 降序，第二优先级是 value 升序）：
No.stepsr(2,3,5,7)value110( 19, 4, 0, 6 )4996238671872210( 4, 20, 0, 5 )93763816684171239( 12, 7, 0, 2 )43893964849( 33, 3, 0, 0 )23192823398458( 11, 7, 0, 0 )447897668( 6, 6, 0, 5 )78414739278( 21, 3, 0, 3 )1942172467288( 1, 2, 0, 12 )24914316961898( 9, 5, 0, 8 )717233481216107( 8, 3, 0, 2 )338688117( 1, 10, 0, 1 )826686127( 10, 7, 0, 0 )2239488137( 1, 13, 0, 0 )3188646147( 4, 10, 0, 1 )6613488157( 9, 4, 0, 3 )14224896167( 6, 27, 0, 1 )3416267673274176177( 24, 18, 0, 0 )6499837226778624186( 10, 3, 0, 0 )27648196( 2, 5, 0, 2 )47628206( 0, 3, 0, 4 )64827216( 6, 3, 0, 2 )84672226( 27, 0, 0, 0 )134217728236( 5, 5, 0, 6 )914838624246( 10, 6, 0, 4 )1792336896256( 23, 2, 0, 2 )3699376128266( 1, 20, 0, 1 )48814981614276( 5, 6, 0, 8 )134481277728286( 16, 8, 0, 3 )147483721728296( 24, 6, 0, 6 )1438916737499136305( 7, 1, 0, 1 )2688315( 7, 1, 0, 2 )18816325( 2, 8, 0, 0 )26244335( 5, 2, 0, 3 )98784345( 3, 4, 0, 3 )222264355( 18, 0, 0, 0 )262144365( 12, 4, 0, 0 )331776375( 2, 5, 0, 3 )333396385( 3, 5, 0, 3 )666792395( 15, 1, 0, 1 )688128405( 16, 3, 0, 0 )1769472415( 6, 8, 0, 1 )2939328425( 9, 1, 0, 4 )3687936435( 12, 1, 0, 3 )4214784445( 11, 0, 0, 4 )4917248455( 5, 10, 0, 1 )13226976465( 7, 2, 0, 5 )19361664475( 2, 4, 0, 6 )38118276485( 15, 7, 0, 0 )71663616495( 16, 5, 0, 1 )111476736505( 1, 4, 0, 7 )133413966515( 2, 0, 0, 9 )161414428525( 21, 4, 0, 0 )169869312535( 5, 0, 0, 8 )184473632545( 3, 14, 0, 1 )267846264555( 6, 0, 0, 8 )368947264565( 7, 12, 0, 1 )476171136575( 20, 5, 0, 1 )1783627776585( 9, 2, 0, 7 )3794886144595( 9, 11, 0, 2 )4444263936605( 19, 2, 0, 4 )11329339392615( 12, 0, 0, 8 )23612624896625( 22, 6, 0, 2 )149824733184635( 9, 13, 0, 3 )279988627968645( 11, 2, 0, 9 )743797684224655( 14, 10, 0, 4 )2322868617216665( 5, 11, 0, 7 )4668421498272675( 14, 1, 0, 10 )13884223438848685( 6, 23, 0, 1 )42176144114496695( 39, 3, 0, 2 )727326941773824705( 35, 2, 0, 6 )36381499733311488714( 1, 3, 0, 1 )378724( 7, 1, 0, 0 )384734( 1, 0, 0, 3 )686744( 8, 1, 0, 0 )768754( 0, 2, 2, 1 )1575764( 2, 2, 0, 2 )1764774( 1, 3, 0, 2 )2646784( 1, 7, 0, 0 )4374794( 11, 1, 0, 0 )6144804( 1, 2, 0, 3 )6174814( 7, 0, 0, 2 )6272824( 10, 0, 0, 1 )7168834( 3, 1, 0, 3 )8232844( 2, 7, 0, 0 )8748854( 8, 2, 0, 1 )16128864( 4, 3, 0, 2 )21168874( 5, 6, 0, 0 )23328884( 4, 5, 0, 1 )27216894( 12, 0, 0, 1 )28672904( 5, 1, 0, 3 )32928914( 4, 7, 0, 0 )34992924( 4, 2, 0, 3 )49392934( 0, 1, 5, 2 )59535944( 2, 0, 0, 5 )67228954( 0, 2, 2, 3 )77175964( 9, 3, 0, 1 )96768974( 8, 2, 0, 2 )112896984( 6, 7, 0, 0 )139968994( 4, 3, 0, 3 )1481761004( 5, 6, 0, 1 )1632961014( 1, 7, 0, 2 )2143261024( 2, 10, 0, 0 )2361961034( 17, 1, 0, 0 )3932161044( 1, 8, 0, 2 )6429781054( 5, 2, 0, 4 )6914881064( 12, 3, 0, 1 )7741441074( 2, 4, 0, 4 )7779241084( 3, 0, 0, 6 )9411921094( 6, 7, 0, 1 )9797761104( 1, 5, 0, 4 )11668861114( 0, 4, 0, 5 )13613671124( 6, 2, 0, 4 )13829761134( 2, 1, 0, 6 )14117881144( 11, 6, 0, 0 )14929921154( 10, 5, 0, 1 )17418241164( 6, 4, 0, 3 )17781121174( 8, 1, 0, 4 )18439681184( 4, 0, 0, 6 )18823841194( 1, 2, 0, 6 )21176821204( 5, 5, 0, 3 )26671681214( 4, 4, 0, 4 )31116961224( 16, 0, 0, 2 )32112641234( 5, 0, 0, 6 )37647681244( 6, 10, 0, 0 )37791361254( 6, 3, 0, 4 )41489281264( 13, 4, 0, 1 )46448641274( 0, 14, 0, 0 )47829691284( 5, 4, 0, 4 )62233921294( 8, 4, 0, 3 )71124481304( 20, 2, 0, 0 )94371841314( 10, 3, 0, 3 )94832641324( 16, 1, 0, 2 )96337921334( 14, 6, 0, 0 )119439361344( 7, 7, 0, 2 )137168641354( 1, 2, 0, 7 )148237741364( 24, 0, 0, 0 )167772161374( 16, 0, 0, 3 )224788481384( 14, 0, 0, 4 )393379841394( 4, 10, 0, 2 )462944161404( 3, 11, 0, 2 )694416241414( 17, 4, 0, 1 )743178241424( 12, 4, 0, 3 )1137991681434( 8, 3, 0, 5 )1161699841444( 4, 11, 0, 2 )1388832481454( 0, 12, 0, 3 )1822842631464( 23, 3, 0, 0 )2264924161474( 8, 3, 0, 6 )8131898881484( 19, 5, 0, 1 )8918138881494( 1, 4, 0, 8 )9338977621504( 0, 19, 0, 0 )11622614671514( 11, 5, 0, 4 )11948912641524( 6, 10, 0, 3 )12962436481534( 26, 3, 0, 0 )18119393281544( 18, 1, 0, 4 )18882232321554( 25, 2, 0, 1 )21139292161564( 4, 10, 0, 4 )22684263841574( 13, 8, 0, 2 )26336378881584( 3, 9, 0, 5 )26464974481594( 17, 2, 0, 4 )28323348481604( 1, 14, 0, 3 )32811167341614( 26, 0, 0, 2 )32883343361624( 2, 10, 0, 5 )39697461721634( 10, 5, 0, 5 )41821194241644( 14, 10, 0, 1 )67722117121654( 4, 13, 0, 3 )87496446241664( 22, 7, 0, 0 )91729428481674( 28, 2, 0, 1 )169114337281684( 3, 4, 0, 9 )261491373361694( 4, 14, 0, 3 )262489338721704( 2, 21, 0, 0 )418414128121714( 2, 11, 0, 6 )833646696121724( 4, 1, 0, 11 )949116836641734( 23, 7, 0, 1 )1284211998721744( 8, 13, 0, 3 )1399943139841754( 25, 6, 0, 1 )1712282664961764( 21, 9, 0, 1 )2889476997121774( 9, 17, 0, 1 )4628383441921784( 15, 3, 0, 7 )7286181396481794( 16, 13, 0, 1 )7313988648961804( 10, 1, 0, 10 )8677639649281814( 29, 5, 0, 1 )9132174213121824( 6, 16, 0, 3 )9449616193921834( 0, 4, 0, 12 )11211442632811844( 14, 18, 0, 0 )63474972917761854( 2, 17, 0, 5 )86818348781641864( 13, 16, 0, 2 )172792981831681874( 8, 11, 0, 7 )373473719861761884( 0, 9, 0, 11 )389197222824691894( 8, 15, 0, 5 )617374924669441904( 36, 5, 0, 1 )1168918299279361914( 31, 3, 0, 4 )1392149224488961924( 3, 26, 0, 1 )1423444863864241934( 15, 1, 0, 11 )1943791281438721944( 10, 15, 0, 5 )2469499698677761954( 24, 5, 0, 6 )4796389124997121964( 4, 7, 0, 12 )4843343217373921974( 0, 10, 0, 12 )8173141679318491984( 12, 16, 0, 5 )29633996384133121994( 2, 26, 0, 3 )34874399164673882004( 5, 25, 0, 3 )92998397772463682014( 0, 32, 0, 1 )129711413219628872024( 7, 16, 0, 8 )317639398742426882034( 17, 1, 0, 14 )2666881638133923842044( 23, 1, 0, 12 )3483273976338186242054( 9, 27, 0, 3 )13391769279234769922064( 55, 2, 0, 1 )22698142121947299842074( 0, 22, 0, 10 )88643726269361176412084( 30, 21, 0, 0 )112317187278734622722094( 31, 12, 0, 5 )191811712299313397762104( 47, 11, 0, 0 )249312238496812892162114( 9, 4, 0, 19 )4727349811277949864962124( 59, 5, 0, 2 )6863918177676863471616
限于篇幅，仅贴出步数不小于 4 的结果。
大家可以在其中找找看，
是否有两组 value 仅仅是数字 1 的个数有所不同，而其它数字数目完全等同的？
:)
又要动用haskell啊
mathe练手吧
http://www.research.att.com/~njas/sequences/A121111
http://www.research.att.com/~njas/sequences/A003001
http://www.mathews-archive.com/digit-related-numbers/persistence.html
似乎这个序列不如我们找到的
哦，似乎他们不要求素数
呵呵，看各位的讨论，有时间我也看看haskell去，
没接触还不知道它有什么特别之处呢？
跟ruby与mathematica相比？
:)
不同的思维
haskell是函数式语言