cp's OEIS Frontend

A334168 Numbers m whose leading digit and the other decimal digits appear respectively before and directly after the decimal point of its m-th root.

%I A334168 #38 Mar 30 2023 07:29:27
%S A334168 1,12,104,1006,10009,100011,1000013,10000016,100000018,1000000020,
%T A334168 10000000023,100000000025,1000000000027,10000000000029,
%U A334168 100000000000032,1000000000000034,10000000000000036,100000000000000039,1000000000000000041,10000000000000000043
%N A334168 Numbers m whose leading digit and the other decimal digits appear respectively before and directly after the decimal point of its m-th root.
%C A334168 These numbers m are equal to the integer part of their m-th root multiplied by 10 to the power of the number of digits of m-1.
%C A334168 The last nonzero digits of the terms are conjectured to be the Beatty sequence for log(10), A059545.
%F A334168 a(n+1) = floor((10^(n/10^n))*10^n) (conjectured).
%F A334168 a(n) = 10^(n-1) + floor((n-1)*log(10)) (conjectured). - _David A. Corneth_, Apr 19 2020
%e A334168 12^(1/12) = 1.23007..., 104^(1/104) = 1.0457..., 100011^(1/100011) = 1.00011512...
%o A334168 (Python)
%o A334168 # for the first 6 terms
%o A334168 import math
%o A334168 for n in range(1, 1000000):
%o A334168     if math.floor((n**(1/n))*10**(len(str(n))-1)) == n:
%o A334168         print(n)
%o A334168 (PARI) isok(m) = floor(10^(#Str(m)-1)*sqrtn(m, m)) == m; \\ _Michel Marcus_, Apr 17 2020
%Y A334168 Cf. A059545.
%K A334168 nonn,base
%O A334168 1,2
%A A334168 _Alaa A. Nasr_, Apr 17 2020
%E A334168 More terms from _David A. Corneth_, Apr 19 2020