lambdaway :: harshad

6 | list | login |load

| |

_h1 harshad or niven | [[zuckerman|?view=zuckerman_numbers]]

_p Following [[https://rosettacode.org/wiki/Harshad_or_Niven_series#JavaScript|https://rosettacode.org/wiki/Harshad_or_Niven_series#JavaScript]] the Harshad or Niven numbers are positive integers ≥ 1 that are divisible by the sum of their digits. For example,   42   is a Harshad number as   42   is divisible by   (4 + 2)   without remainder.

_p Task: Assume that the series is defined as the numbers in increasing order. The task is to create a function/method/procedure to generate successive members of the Harshad sequence. Use it to:
_ul  list the first 20 members of the sequence,   and
_ul  list the first Harshad number greater than 1000.

{prewrap
'{def harshad?
 {def harshad?.sum
  {lambda {:n}
  {if {W.empty? {W.rest :n}}
   then {W.first :n}
   else {+ {W.first :n}
           {harshad?.sum {W.rest :n}}} }}}
 {lambda {:n}
  {= {% :n {harshad?.sum :n}} 0} }} 
-> {def harshad?
 {def harshad?.sum
  {lambda {:n}
  {if {W.empty? {W.rest :n}}
   then {W.first :n}
   else {+ {W.first :n}
           {harshad?.sum {W.rest :n}}} }}}
 {lambda {:n}
  {= {% :n {harshad?.sum :n}} 0} }}

'{harshad? 12}
-> {harshad? 12}
'{harshad? 13}
-> {harshad? 13}

'{def harshads
 {def harshads.loop
  {lambda {:a :n :i}
   {if {> {A.length :a} :n}
    then :a
    else {harshads.loop {if {harshad? :i} 
                         then {A.addlast! :i :a} 
                         else :a}
                        :n 
                        {+ :i 1}} }}}
 {lambda {:n}
  {harshads.loop {A.new} :n 0} }} 
-> {def harshads
 {def harshads.loop
  {lambda {:a :n :i}
   {if {> {A.length :a} :n}
    then :a
    else {harshads.loop {if {harshad? :i} 
                         then {A.addlast! :i :a} 
                         else :a}
                        :n 
                        {+ :i 1}} }}}
 {lambda {:n}
  {harshads.loop {A.new} :n 0} }}

'{harshads 20}
-> {harshads 20}

'{def firstharshadafter
 {def firstharshadafter.loop
  {lambda {:i}
   {if {harshad? :i}
    then :i
    else {firstharshadafter.loop {+ :i 1}} }}}
 {lambda {:n}
  {firstharshadafter.loop {+ :n 1}} }}
-> {def firstharshadafter
 {def firstharshadafter.loop
  {lambda {:i}
   {if {harshad? :i}
    then :i
    else {firstharshadafter.loop {+ :i 1}}}}}
 {lambda {:n}
  {firstharshadafter.loop {+ :n 1}}}}

'{firstharshadafter 1000}
-> {firstharshadafter 1000}
}

{script 
function isHarshad(n) {
    var s = 0;
    var n_str = new String(n);
    for (var i = 0; i < n_str.length; ++i) {
        s += parseInt(n_str.charAt(i));
    }
    return n % s === 0;
}

var count = 0;
var harshads = [];

for (var n = 1; count < 20; ++n) {
    if (isHarshad(n)) {
        count++;
        harshads.push(n);
    }
}

// alert(harshads.join(" "));

var h = 1000;
while (!isHarshad(++h));
// alert(h);

LAMBDATALK.DICT["isharshad"] = function() {
  return (isHarshad( Number( arguments[0].trim() )) )? "true" : "false"
};
}