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A153042
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a(n)...a(1) = digital representation of n-digit number m, the cube of which, m^3, ends with n 1's.
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9
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1, 7, 4, 8, 8, 2, 8, 6, 3, 7, 3, 6, 6, 1, 7, 8, 5, 8, 9, 7, 2, 8, 7, 7, 5, 3, 8, 3, 9, 8, 9, 8, 7, 2, 7, 1, 7, 1, 1, 6, 3, 2, 9, 2, 2, 2, 7, 7, 3, 7, 3, 0, 0, 3, 1, 8, 6, 7, 8, 4, 5, 6, 2, 5, 2, 2, 3, 0, 3, 8, 5, 9, 7, 9, 0, 3, 6, 3, 3, 8, 0, 8, 0, 0, 2, 5, 0, 1, 1, 2, 2, 6, 9, 1, 2, 2, 1, 1, 9, 1, 8, 8, 5, 7, 7
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OFFSET
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1,2
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COMMENTS
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For any n there is only one solution. Case a(n)=0 means that cube of (n-1)-digit number ends with n (not (n-1)) 1's. Case a(n+1)=a(n)=0 means that cube of (n-1)-digit number ends with (n+1) (not (n-1)) 1's, etc.
10-adic digits of the cubic root of -1/9. - Max Alekseyev, Jul 12 2022
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LINKS
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EXAMPLE
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1^3= 1; 71^3 = 357911; 471^3 = 104487111; 8471^3 = 607860671111.
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MAPLE
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N:= 200:
op([1, 3], padic:-rootp(9*x^3+1, 10, N+2))[1..N+1]; # Robert Israel, Mar 25 2018
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PROG
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(PARI) n=0; for(i=1, 100, m=(10^i-1)/9; for(x=0, 9, if(((n+(x*10^(i-1)))^3)%(10^i)==m, n=n+(x*10^(i-1)); print1(x", "); break))) \\ Aswini Vaidyanathan, May 07 2013
(PARI) digits(sqrtn(-1/9 + O(10^100), 3)) \\ Max Alekseyev, Jul 12 2022
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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