A060376 If 10^n can be written as x*y where the digits of x and y are all nonzero, then let a(n) = smallest such x, otherwise a(n) = -1.

1, 2, 4, 8, 16, 32, 64, 128, -1, 512, -1, -1, -1, -1, -1, -1, -1, -1, 262144, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8589934592, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1

Offset

0,2

Comments

According to Ogilvy and Anderson, 10^33 is the highest known power of ten that can be expressed as the product of two zero-free factors. "If there is another one, it is greater than 10^5000." p. 89

References

C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, 1966, p. 89.

Rudolph Ondrejka, Nonzero factors of 10^n, Recreational Mathematics Magazine, no. 6 (1961), p. 59.

Links

Table of n, a(n) for n=0..79.

Example

10^2 = 4 * 25, so a(2) = 4.

Crossrefs

Cf. A060391 (for values of y).

Sequence in context: A251761 A133024 A243085 * A047869 A270201 A016025

Adjacent sequences: A060373 A060374 A060375 * A060377 A060378 A060379

Keyword

sign,base

Author

Jason Earls, Apr 02 2001

Status

approved