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a(n+1) is the next smallest nontrivial cube beginning with a(n), initial term is 3.
6

%I #28 Apr 17 2020 02:50:46

%S 3,343,34328125,343281258441879199985152,

%T 3432812584418791999851522633552283890505384030397984598615707004422070464

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

%C Terms a(6) and a(7) are 219 and 658 digits long, respectively. - _Jon E. Schoenfield_, Aug 06 2017

%H Jon E. Schoenfield, <a href="/A249799/b249799.txt">Table of n, a(n) for n = 1..7</a>

%o (Python)

%o def f(x):

%o n = x

%o s = 1

%o while s < 10**7:

%o if s % 10:

%o S = str(s**3)

%o if S.startswith(str(n)):

%o print(s**3,end=', ')

%o n = s**3

%o s += 1

%o f(3)

%o (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 a(3)

%Y Cf. A048559, A048561, A249894.

%K nonn,base

%O 1,1

%A _Derek Orr_, Dec 03 2014