A030289 a(n+1) is the next larger cube with no digits in common with a(n), a(0) = 0.

0, 1, 8, 27, 64, 125, 343, 512, 4096, 5832, 64000, 91125, 300763, 941192, 3375000, 8489664, 13312053, 86444696669696, 100175333300307, 488224224494488, 510657175657000, 2233398984434344, 5177717000000000, 6393843393228864

Offset: 0

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

From a(24) on, even-indexed terms are powers of 1000, odd-indexed terms are the next larger cube to a(n-1)*20/9 with no digit 0 or 1, cf. A030290. - M. F. Hasler, Nov 12 2017

Links

• David W. Wilson, Table of n, a(n) for n = 0..90

Crossrefs

Squares whose digits do not appear in previous term: A030288.

Primes whose digits do not appear in previous term: A030284.

Cf. A030290: cube roots of the terms.

Programs

Mathematica

bb={0}; idi1=IntegerDigits[0]; Do[idi=IntegerDigits[r=i^3]; If[Intersection[idi, idi1]=={}, bb={bb, r}; idi1=idi], {i, 1, 100000}]; fla=Flatten[bb] (* Zak Seidov, Feb 17 2005 *)
Nest[Append[#, Block[{k = Last@ # + 1, m = IntegerDigits[Last[#]^3]}, While[IntersectingQ[IntegerDigits[k^3], m], k++]; k]] &, {0}, 23]^3 (* Michael De Vlieger, Nov 13 2017 *)

PARI

next_A030289(n,D(n)=Set(digits(n)),S=D(n))={if(n>6e15,S[1]&&return(1000^(logint(n,1000)+1));n=n*20\9); for(k=sqrtnint(n,3)+1,oo,#setintersect(D(k^3),S)||return(k^3))} \\ M. F. Hasler, Nov 12 2017

Formula

a(n) = A030290(n)^3. - David W. Wilson, Nov 08 2017