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A249799 a(n+1) is the next smallest nontrivial cube beginning with a(n), initial term is 3.

%I A249799 #28 Apr 17 2020 02:50:46
%S A249799 3,343,34328125,343281258441879199985152,
%T A249799 3432812584418791999851522633552283890505384030397984598615707004422070464
%N A249799 a(n+1) is the next smallest nontrivial cube beginning with a(n), initial term is 3.
%C A249799 Terms a(6) and a(7) are 219 and 658 digits long, respectively. - _Jon E. Schoenfield_, Aug 06 2017
%H A249799 Jon E. Schoenfield, <a href="/A249799/b249799.txt">Table of n, a(n) for n = 1..7</a>
%o A249799 (Python)
%o A249799 def f(x):
%o A249799     n = x
%o A249799     s = 1
%o A249799     while s < 10**7:
%o A249799         if s % 10:
%o A249799             S = str(s**3)
%o A249799             if S.startswith(str(n)):
%o A249799                 print(s**3,end=', ')
%o A249799                 n = s**3
%o A249799         s += 1
%o A249799 f(3)
%o A249799 (PARI) a(n)=k=n;s=1;while(s<10^7,if(s%10,if(s^3\(10^(#Str(s^3)-#Str(k)))==k,print1(s^3,", ");k=s^3));s++)
%o A249799 a(3)
%Y A249799 Cf. A048559, A048561, A249894.
%K A249799 nonn,base
%O A249799 1,1
%A A249799 _Derek Orr_, Dec 03 2014