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A030289
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a(n+1) is the next larger cube with no digits in common with a(n), a(0) = 0.
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3
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0, 1, 8, 27, 64, 125, 343, 512, 4096, 5832, 64000, 91125, 300763, 941192, 3375000, 8489664, 13312053, 86444696669696, 100175333300307, 488224224494488, 510657175657000, 2233398984434344, 5177717000000000, 6393843393228864
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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