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A060159 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). 13
12, 20, 110, 510, 131052, 12751220, 10000095, 2162049150, 124324220, 1, 920067411130599, 43494229746440272890, 12100324200007455010742303399999999999999999990, 4201420328711160916072939999999999999999999999999999999999999996 (list; graph; refs; listen; history; text; internal format)
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
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.
EXAMPLE
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.
CROSSREFS
Cf. A005349.
Sequence in context: A181701 A025104 A163323 * A167351 A231400 A231467
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

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)