lambdaway :: factorions

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_h1 factorions

_p Following [[rosettacode|https://rosettacode.org/wiki/Factorions]], a factorion is a natural number that equals the sum of the factorials of its digits. Example: {b 1! + 4! + 5!   =   1 + 24 + 120   =   145}

{prewrap
;; {def fact {lambda {:n} {if {= :n 0} then 1 else {* {S.serie 1 :n}}}}}

'{def facts
 {S.first
  {S.map {{lambda {:a :i} 
                  {A.addlast! {* {A.get {- :i 1} :a} :i} :a}
          } {A.new 1}}
         {S.serie 1 11}}}}
-> {def facts
 {S.first
  {S.map {{lambda {:a :i} 
                  {A.addlast! {* {A.get {- :i 1} :a} :i} :a}
          } {A.new 1}}
         {S.serie 1 11}}}}

'{def sumfacts
 {def sumfacts.r
  {lambda {:base :sum :i}
   {if {> :i 0}
    then {sumfacts.r :base
                     {+ :sum {A.get {% :i :base} {facts}}}
                     {floor {/ :i :base}}}
    else :sum }}}
 {lambda {:b :n}
  {sumfacts.r :b 0 :n}}} 
-> {def sumfacts
 {def sumfacts.r
  {lambda {:base :sum :i}
   {if {> :i 0}
    then {sumfacts.r :base
                     {+ :sum {A.get {% :i :base} {facts}}}
                     {floor {/ :i :base}}}
    else :sum }}}
 {lambda {:b :n}
  {sumfacts.r :b 0 :n}}}

'{def show
 {lambda {:base}
  {S.replace \s by space in
   {S.map {{lambda {:base :i}
                   {if {= {sumfacts :base :i} :i} then :i else}
           } :base}
          {S.serie 1 50000}}}}}
-> {def show
 {lambda {:b}
  {S.replace \s by space in
   {S.map {{lambda {:b :i} {if {= {sumfacts :b :i} :i} then :i else}} :b}
       {S.serie 1 50000}}}}}

'{S.map {lambda {:base}
               {div}factorions for base :base: {show :base}} 
       9 10 11 12}
->
factorions for base 9: 1 2 41282 
factorions for base 10: 1 2 145 40585 
factorions for base 11: 1 2 26 48 40472 
factorions for base 12: 1 2 
}