A247883 Consecutive exclusionary cubes: Digits of n are not present in n^3 and digits of n+1 are not present in (n+1)^3.

2, 7, 47, 52, 187, 222, 477, 587, 5522, 6777

Offset: 1

Author

Derek Orr, Sep 25 2014

Keywords

• nonn
• base
• more

Comments

If it exists, a(11) > 10^7.

All terms == 2 (mod 5). - Robert Israel, Mar 10 2025

Crossrefs

Cf. A029785.

Programs

Maple

filter:= proc(n) convert(convert(n,base,10),set) intersect convert(convert(n^3,base,10),set) = {} end proc:
select(t -> filter(t) and filter(t+1), [seq(i,i=2..10^6, 5)]); # Robert Israel, Mar 10 2025

PARI

for(n=1,10^6,s=digits(n);t=digits(n+1);s3=digits(n^3);t3=digits((n+1)^3);if(#vecsort(concat(s,s3),,8)==#vecsort(s,,8)+#vecsort(s3,,8)&&#vecsort(concat(t,t3),,8)==#vecsort(t,,8)+#vecsort(t3,,8),print1(n,", ")))

Python

for n in range(10**6):
  s, t = str(n), str(n+1)
  s3, t3 = str(n**3), str((n+1)**3)
  c = 0
  for i in s:
    if s3.count(i):
      c += 1
      break
  for j in t:
    if t3.count(j):
      c += 1
      break
  if not c:
    print(n, end=', ')

Extensions

Definition corrected by Robert Israel, Mar 10 2025