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.

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

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*(9-q) 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: A282648 A139540 A343550 * A135363 A118717 A181529

Adjacent sequences: A285173 A285174 A285175 * A285177 A285178 A285179

Keyword

nonn,base

Author

Matthew Scroggs, Apr 18 2017

Status

approved