

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
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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

Table of n, a(n) for n=1..14.
C. N. Cooper and R. E. Kennedy, On consecutive Niven numbers, Fibonacci Quart, (1993) 21, 146151.
H. G. Grundman, Sequences of consecutive nNiven numbers, Fibonacci Quarterly, (1994), 32 (2): 174175.
B. Wilson, Construction of 2n Consecutive nNiven Numbers, Fibonacci Quarterly, (1997), 35, 122128.
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
Adjacent sequences: A060156 A060157 A060158 * A060160 A060161 A060162


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



