OFFSET
1,1
COMMENTS
Cooper and Kennedy (1993) proved that this sequence contains 20 terms. - Sergio Pimentel, Sep 18 2008
a(16) = 50757686696033684694106416498959861492*10^280 - 9 and a(17) = 14107593985876801556467795907102490773681*10^280 - 10. - Max Alekseyev, Apr 07 2013
H. G. Grundman (1994) extended the Cooper and Kennedy result to show that there are 2b but not 2b + 1 consecutive Harshad numbers in any base b. - Jianing Song, Dec 16 2024
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 110, p. 39, Ellipses, Paris 2008.
LINKS
C. N. Cooper and R. E. Kennedy, On consecutive Niven numbers, Fibonacci Quart, (1993) 21, 146-151.
H. G. Grundman, Sequences of consecutive n-Niven numbers, Fibonacci Quarterly, (1994), 32 (2): 174-175.
B. Wilson, Construction of 2n Consecutive n-Niven Numbers, Fibonacci Quarterly, (1997), 35, 122-128.
Carlos Rivera, Puzzle 129. Earliest sets of K consecutive Harshad Numbers, The Prime Puzzles and Problems Connection.
Wikipedia, Harshad number
EXAMPLE
a(3) = 110 since (110, 111, 112) is the earliest run of 3 consecutive Harshad numbers: 110 is divisible by 1+1+0=2, 111 is divisible by 1+1+1=3, 112 is divisible by 1+1+2=4, but 109 is not divisible by 1+0+9=10, 113 is not divisible by 1+1+3=5, and there are no earlier runs of 3 consecutive numbers with this property. [Clarified by Jianing Song, Dec 16 2024]
CROSSREFS
KEYWORD
fini,hard,nonn,base
AUTHOR
Carlos Rivera, Mar 12 2001
EXTENSIONS
a(8) is found by Jud McCranie, Nov 13 2001
a(11)-a(13) are found by Giovanni Resta, Feb 21 2008
a(14), a(16)-a(17) from Max Alekseyev, Apr 07 2013
STATUS
approved