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A002780
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Numbers whose cube is a palindrome.
(Formerly M1736 N0688)
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9
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0, 1, 2, 7, 11, 101, 111, 1001, 2201, 10001, 10101, 11011, 100001, 101101, 110011, 1000001, 1001001, 1100011, 10000001, 10011001, 10100101, 11000011, 100000001, 100010001, 100101001, 101000101, 110000011, 1000000001, 1000110001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(8)=2201 is the only known non-palindromic rootnumber.
There are no further non-palindromic terms (other than 2201) up to 10^11. - Matevz Markovic, Apr 04 2011. There are none up to 10^15, by direct search. - Charles Greathouse, May 16 2011
There are no non-palindromic terms in the range 10^15 to 10^20 with digits from the set {0,1,2}. - Hans Havermann, May 18 2011.
Contribution from Vladimir Shevelev, May 23 2011: (Start)
Using the table by Noe-De Geest, I noticed that all numbers {a(n)=A002780(n); 11<=a(n)<=10^17+10^16+11}, except 2201, allow a partition into 3 disjoint classes of terms of the following forms: 10^k+1, 10^(2*k)+10^k+1, and (10^u+1)*(10^v+1).
Does there exist a term a(n)>10^17+10^16+11 which is in none of these classes?
If there is no such term, then we conclude that the sum of digits of a(n) does not exceed 4 (more exactly, it is i+1 where i is the number of class).
One can prove that the sequence contains no term (other than 2201) with sum of digits = 5. (End)
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REFERENCES
| G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..89 (from De Geest)
P. De Geest, Palindromic Cubes
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CROSSREFS
| Cf. A002781 (cube of these numbers).
Sequence in context: A101592 A135066 A085315 * A069885 A069748 A064441
Adjacent sequences: A002777 A002778 A002779 * A002781 A002782 A002783
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KEYWORD
| base,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Patrick De Geest.
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