

A285176


Elastic numbers: numbers n with two or more digits such that for any number m made by inserting any number of 0's between the digits of n, m is a multiple of n.


1



10, 15, 18, 20, 30, 40, 45, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700
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OFFSET

1,1


COMMENTS

15, 18 and 45 are the only elastic numbers with no 0 as a digit. Proof: let n = 10*m+k, 0<k<10. Then n is elastic only if 90*m is a multiple of n, i.e., 90*m = n*q = (10*m+k)*q = 10*m*q + k*q. It follows that q<9, so k*q<100. But k*q = 10*m*(9q) which is no less than 100 if n has at least 3 digits. Contradiction.  Andrey Zabolotskiy, Apr 18 2017


REFERENCES

D. Griller, Elastic Numbers, Rational Falcon, 2017, 45 & 95.


LINKS

Table of n, a(n) for n=1..19.


EXAMPLE

15 is an elastic number because 105, 1005, 10005, 100005, ... are all multiples of 15.


CROSSREFS

Sequence in context: A269985 A282648 A139540 * A135363 A118717 A181529
Adjacent sequences: A285173 A285174 A285175 * A285177 A285178 A285179


KEYWORD

nonn,base


AUTHOR

Matthew Scroggs, Apr 18 2017


STATUS

approved



