Harshad Number

May 27, 2014, 9:25 PM

# The German geek podcast Fanboys asked their audience in their latest episode 135 to check which of the episode numbers for upcoming shows will be a 2-level Harshad Number.
# A Harshad Number in a given number base, is an integer that is divisible by the sum of its digits when written in that base.
# A 2-level Harshad Number, according to the Fanboys interpretation, shall be a number which divisible by the sum of its digits, and the resulting ratio itself shall be a Harshad Number.
# http://stackoverflow.com/questions/18674535/function-for-multi-level-harshad-number-in-r

multi.step.harshed.number = function(numlevels, start, end) {
  library(parallel)
  processors= detectCores()
  cl= makeCluster(processors)
  is.integer= function(x) ifelse (x== as.integer(x), return (x), return(NA))
  digitsum = function(x) sum(floor(x/10^(0:(nchar(x)-1))) %% 10)
  digitsumratio= function(x) ifelse(is.integer(x/digitsum(x)), x/digitsum(x), NA) 
  multi.digitsumratio= function(iter, x) {
    for (i in 1:iter) x= digitsumratio(x)
    return (ifelse(is.na(x), FALSE, TRUE))     
  }
  sequence=start:end
  idx=parSapply(cl=cl,X=sequence, FUN=function (x) multi.digitsumratio(numlevels, x))
  sequence[idx]
}

multi.step.harshed.number(42, 100, 10000)

 [1]   100   108   120   162   180   200   210   216   240   243   270
[12]   300   324   360   378   400   405   420   432   450   480   486
[23]   500   540   600   630   648   700   720   756   800   810   840
[34]   864   900   972  1000  1080  1200  1296  1458  1620  1800  1944
[45]  2000  2100  2160  2400  2430  2700  2916  3000  3240  3402  3600
[56]  3780  4000  4050  4200  4320  4374  4500  4800  4860  5000  5400
[67]  5832  6000  6300  6480  6804  7000  7200  7290  7560  8000  8100
[78]  8400  8640  8748  9000  9720 10000