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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). 5
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. [From 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 (1993). On consecutive Niven numbers. Fibonacci Quart, 21, 146-151.

H. G. Grundman (1994). Sequences of consecutive n-Niven numbers. Fibonacci Quarterly 32 (2): 174-175.

B. Wilson (1997). Construction of 2n Consecutive n-Niven Numbers. Fibonacci Quarterly, 35, 122-128.

C. Rivera, Puzzle 129.  Earliest sets of K consecutive Harshad Numbers

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

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Last modified December 19 11:35 EST 2014. Contains 252218 sequences.