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

5, 1, 2, 12, 0

Offset

0,1

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

Links

Table of n, a(n) for n=0..4.

Example

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.

Prog

(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

Crossrefs

Cf. A001597, A097056.

Sequence in context: A226613 A274989 A328199 * A088781 A085608 A258339

Adjacent sequences: A289687 A289688 A289689 * A289691 A289692 A289693

Keyword

nonn,fini

Author

Wolfram Hüttermann, Jul 09 2017

Status

approved