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

9, 9261, 92615351886784, 9261535188678457128255779014690172977343833, 926153518867845712825577901469017297734383369607525414854584903918819898290730346512973206455943454340951813592133138664220381927

Offset: 1

Author

Derek Orr, Dec 03 2014

Keywords

• nonn
• base

Comments

a(7) has 1163 digits. - Robert Israel, Dec 04 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..6

Crossrefs

Cf. A249799, A048559, A048561.

Programs

Maple

nextterm:= proc(x) local d,s,t;
   for d from 1 do
     s:= traperror(ceil((x*10^d+1)^(1/3)));
     while not type(s,integer) do
        Digits:= Digits *2;
        s:= traperror(ceil((x*10^d+1)^(1/3)));
     od:
     t:= traperror(floor(((x+1)*10^d-1)^(1/3)));
     while not type(t,integer) do
        Digits:= Digits *2;
        t:= traperror(floor(((x+1)*10^d-1)^(1/3)));
     od:
     if s <= t then return s^3 fi;
   od:
end proc:
a[1]:= 9;
for n from 2 to 6 do a[n]:= nextterm(a[n-1]) od; # Robert Israel, Dec 04 2014

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++)
a(9)

Python

def f(x):
  n = x
  s = 1
  while s < 10**7:
    if s % 10:
      S = str(s**3)
      if S.startswith(str(n)):
        print(s**3, end=', ')
        n = s**3
    s += 1
f(9)

Extensions

a(4) and a(5) from Robert Israel, Dec 04 2014