Note: &nbsp; '''[[wp:Harshad_number|Niven]]''' &nbsp; numbers are also called &nbsp; '''Harshad'''      &nbsp; numbers.
:::: &nbsp; They are also called&nbsp;                  &nbsp; '''multidigital''' &nbsp; numbers.


'''Niven''' numbers are positive integers which are evenly divisible by the sum of its
digits &nbsp; (expressed in base ten).

''Evenly divisible'' &nbsp; means &nbsp; ''divisible with no remainder''.


;Task:
:* &nbsp; find the gap (difference) of a Niven number from the previous Niven number
:* &nbsp; if the gap is &nbsp; ''larger'' &nbsp; than the (highest) previous gap, &nbsp; then:
:::* &nbsp; show the index (occurrence) of the gap &nbsp; &nbsp;  (the 1st gap is &nbsp; '''1''')
:::* &nbsp; show the index of the Niven number that starts the gap &nbsp; &nbsp; (1<sup>st</sup> Niven number is &nbsp; '''1''', &nbsp; 33<sup>rd</sup> Niven number is &nbsp; '''100''')
:::* &nbsp; show the Niven number that starts the gap
:::* &nbsp; show all numbers with comma separators where appropriate &nbsp; (optional)
:::* &nbsp; I.E.: &nbsp; the gap size of &nbsp; '''60''' &nbsp; starts at the &nbsp; 33,494<sup>th</sup> &nbsp; Niven number which is Niven number &nbsp; '''297,864'''
:* &nbsp; show all increasing gaps up to the &nbsp; ten millionth &nbsp; ('''10,000,000<sup>th</sup>''') &nbsp; Niven number
:* &nbsp; (optional) &nbsp; show all gaps up to whatever limit is feasible/practical/realistic/reasonable/sensible/viable on your computer
:* &nbsp; show all output here, on this page


;Related task:
:* &nbsp; [https://rosettacode.org/wiki/Harshad_or_Niven_series Harshad or Niven series].


;Also see:
:* &nbsp; [https://cs.uwaterloo.ca/journals/JIS/VOL6/Doyon/doyon.html Journal of Integer Sequences, Vol. 6 (2004), Article 03.2.5, <big>Large and Small Gaps Between Consecutive Niven Numbers</big>].
:* &nbsp; [https://cs.uwaterloo.ca/journals/JIS/VOL6/Doyon/doyon.pdf (PDF) version of the (above) article by Doyon].
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