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A249837 a(n+1) is the next smallest nontrivial cube beginning with a(n), initial term is 9.

%I A249837 #30 Aug 08 2025 14:20:04
%S A249837 9,9261,92615351886784,9261535188678457128255779014690172977343833,
%T A249837 926153518867845712825577901469017297734383369607525414854584903918819898290730346512973206455943454340951813592133138664220381927
%N A249837 a(n+1) is the next smallest nontrivial cube beginning with a(n), initial term is 9.
%C A249837 a(7) has 1163 digits. - _Robert Israel_, Dec 04 2014
%H A249837 Robert Israel, <a href="/A249837/b249837.txt">Table of n, a(n) for n = 1..6</a>
%p A249837 nextterm:= proc(x) local d,s,t;
%p A249837    for d from 1 do
%p A249837      s:= traperror(ceil((x*10^d+1)^(1/3)));
%p A249837      while not type(s,integer) do
%p A249837         Digits:= Digits *2;
%p A249837         s:= traperror(ceil((x*10^d+1)^(1/3)));
%p A249837      od:
%p A249837      t:= traperror(floor(((x+1)*10^d-1)^(1/3)));
%p A249837      while not type(t,integer) do
%p A249837         Digits:= Digits *2;
%p A249837         t:= traperror(floor(((x+1)*10^d-1)^(1/3)));
%p A249837      od:
%p A249837      if s <= t then return s^3 fi;
%p A249837    od:
%p A249837 end proc:
%p A249837 a[1]:= 9;
%p A249837 for n from 2 to 6 do a[n]:= nextterm(a[n-1]) od; # _Robert Israel_, Dec 04 2014
%o A249837 (Python)
%o A249837 def f(x):
%o A249837   n = x
%o A249837   s = 1
%o A249837   while s < 10**7:
%o A249837     if s % 10:
%o A249837       S = str(s**3)
%o A249837       if S.startswith(str(n)):
%o A249837         print(s**3, end=', ')
%o A249837         n = s**3
%o A249837     s += 1
%o A249837 f(9)
%o A249837 (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 A249837 a(9)
%Y A249837 Cf. A249799, A048559, A048561.
%K A249837 nonn,base
%O A249837 1,1
%A A249837 _Derek Orr_, Dec 03 2014
%E A249837 a(4) and a(5) from _Robert Israel_, Dec 04 2014