lambdaway :: curzon

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_h1 [[bigint]] | curzon numbers

_p A Curzon number is defined to be a positive integer n for which {b 2{sup n}+1} is evenly divisible by 2n+1. Generalized Curzon numbers are those where the positive integer n, using a base integer k, satisfy the condition that k{sup n}+1 is evenly divisible by kn+1.

_p Following [[https://rosettacode.org/wiki/Curzon_numbers|https://rosettacode.org/wiki/Curzon_numbers]], find and show the first 50 Generalized Curzon numbers for even base integers from 2 through 10.

{pre 
'{def is_curzon
  {lambda {:n :k}
   {= {BI.% {BI.+ {BI.** :k :n} 1}
            {BI.+ {BI.* :k :n} 1} } 0}}}
-> {def is_curzon
  {lambda {:n :k}
   {= {BI.% {BI.+ {BI.** :k :n} 1}
            {BI.+ {BI.* :k :n} 1} } 0}}}

'{def curzon
 {lambda {:length :base}
  {S.replace \s by space in
   {S.brmap {{lambda {:length :base :count :i}
                   {if {< {A.get 0 :count} :length}
                    then {if {is_curzon :i :base} 
                    then {{lambda {:a :i} :i}
                          {A.set! 0 {+ {A.get 0 :count} 1} :count} :i}
                    else} 
                    else _break_}
           } :length :base {A.new 0}}
          1 100000 1 }}}}  
-> {def curzon
 {lambda {:length :base}
  {S.replace \s by space in
   {S.brmap {{lambda {:length :base :count :i}
                   {if {< {A.get 0 :count} :length}
                    then {if {is_curzon :i :base} 
                          then {{lambda {:a :i} :i}
                                 {A.set! 0 {+ {A.get 0 :count} 1} :count} :i}
                          else} 
                    else _break_}
           } :length :base {A.new 0}}
          1 100000 1 }}}}

}

{prewrap
'{S.map {lambda {:i} 
          {div {b First 50 Curzon numbers using a base of :i:}
          {div {curzon 50 :i}}}}
       {S.serie 2 10 2}}
-> 
{S.map {lambda {:i} 
          {div {b First 50 Curzon numbers using a base of :i:}
          {div {curzon 50 :i}}}}
       {S.serie 2 10 2}}

'{S.last {curzon 1000 6}} -> 20717 in 272193ms = {/ 272193 1000 60} minutes
}

{hr}
_h2 control
{prewrap
First 50 Curzon numbers using a base of 2: 1 2 5   ...  249  254 / Thousandth: 8646
First 50 Curzon numbers using a base of 4: 1 3 7   ...  277  279 / Thousandth: 9375
First 50 Curzon numbers using a base of 6: 1 6 30  ...  670  685 / Thousandth: 20717
First 50 Curzon numbers using a base of 8: 1 14 35 ...  696  735 / Thousandth: 22176
First 50 Curzon numbers using a base of 10: 1 9 10 ... 1785 1837 / Thousandth: 46845 
}

{script 
LAMBDATALK.DICT['BigInt'] = function() {
  var args = arguments[0].trim();
  return BigInt( Number(args) )
};

LAMBDATALK.DICT['BI.+'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) + BigInt( args[1] )
};
LAMBDATALK.DICT['BI.-'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) - BigInt( args[1] )
};
LAMBDATALK.DICT['BI.*'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) * BigInt( args[1] )
};
LAMBDATALK.DICT['BI./'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) / BigInt( args[1] )
};
LAMBDATALK.DICT['BI.%'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) % BigInt( args[1] )
};
LAMBDATALK.DICT['BI.**'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) ** BigInt( args[1] )
};
}

{script 
LAMBDATALK.DICT['S.brmap'] = function () { 
  var args = LAMBDATALK.supertrim(arguments[0]).split(' ');
  var func = args[0],
         a = parseInt( args[1] ),
         b = parseInt( args[2] ),
         c = parseInt( args[3] || 1 ),
         s = '';
  if (b < a) 
    return 'bad interval';
  if (LAMBDATALK.DICT[func] === undefined) 
    return func + ' is undefined';
  for (var i=a; i< b; i=i+c) {
      var value = LAMBDATALK.eval_forms( "{" + func + " " + i + "}" );
      if (value === "_break_") break;
      s += value + ' ';
    }
  return s
};
}