OFFSET
1,3
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 R Greathouse IV, 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.
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)
REFERENCES
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).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..89 (from De Geest)
Patrick De Geest, Palindromic Cubes
G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy]
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]
PROG
(PARI) isok(k) = my(d=digits(k^3)); Vecrev(d) == d; \\ Michel Marcus, Aug 02 2022
(Python)
def ispal(s): return s == s[::-1]
def ok(n): return ispal(str(n**3))
print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, Aug 02 2022
CROSSREFS
KEYWORD
base,nonn,nice
AUTHOR
EXTENSIONS
More terms from Patrick De Geest
STATUS
approved