Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #24 Mar 14 2021 18:45:57
%S 5,1,2,12,0
%N Least k such that there are exactly n perfect powers between 10k and 10k + 10.
%C 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.
%C Further, a(6), ..., a(10) cannot exist because of the Mihailescu theorem, as the only adjoining perfect powers are 8 and 9.
%C a(5) is extremely unlikely to exist; if it does, it is larger than 10^70. - _Charles R Greathouse IV_, Jul 21 2017
%e 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.
%o (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
%Y Cf. A001597, A097056.
%K nonn,fini
%O 0,1
%A _Wolfram Hüttermann_, Jul 09 2017