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A060159
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Initial term of a series of exactly n consecutive Harshad or Niven numbers (a Harshad number is such that is divided by the sum of its digits).
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13
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12, 20, 110, 510, 131052, 12751220, 10000095, 2162049150, 124324220, 1, 920067411130599, 43494229746440272890, 12100324200007455010742303399999999999999999990, 4201420328711160916072939999999999999999999999999999999999999996
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 110, p. 39, Ellipses, Paris 2008.
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LINKS
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Table of n, a(n) for n=1..14.
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.
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EXAMPLE
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a(3)=110 since 110 is divisible by 2, 111 is divisible by 3, 112 is divisible by 4 but 113 is not divisible by 5.
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CROSSREFS
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Cf. A005349.
Sequence in context: A181701 A025104 A163323 * A167351 A231400 A231467
Adjacent sequences: A060156 A060157 A060158 * A060160 A060161 A060162
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KEYWORD
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fini,hard,nonn,base
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AUTHOR
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Carlos Rivera, Mar 12 2001
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EXTENSIONS
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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
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STATUS
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approved
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