A289690 Least k such that there are exactly n perfect powers between 10k and 10k + 10.

5, 1, 2, 12, 0

Offset: 0

Author

Wolfram Hüttermann, Jul 09 2017

Keywords

• nonn
• fini

Comments

I do not know if a(5) exists. If it does, the numbers 10k+1, 10k+3, 10k+5, 10k+7, 10k+9 will be perfect powers. But those numbers are very scarce.

Further, a(6), ..., a(10) cannot exist because of the Mihailescu theorem, as the only adjoining perfect powers are 8 and 9.

a(5) is extremely unlikely to exist; if it does, it is larger than 10^70. - Charles R Greathouse IV, Jul 21 2017

Examples

			If n=2, then there are 2 power numbers between 20 and 30: 25 and 27, and this is the least k with this property.
		

Crossrefs

Cf. A001597, A097056.

Programs

PARI

a(n)=my(k=0); while(sum(j=10*k+1, 10*k+9, (j==1) || ispower(j)) !=n, k++); k; \\ Michel Marcus, Jul 20 2017