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A263613
Palindromic numbers in base 4 that are cubes.
1
0, 1, 1331, 1030301, 1003003001, 1000300030001, 1000030000300001, 1000003000003000001, 1000000300000030000001, 1000000030000000300000001, 1000000003000000003000000001, 1000000000300000000030000000001, 1000000000030000000000300000000001, 1000000000003000000000003000000000001
OFFSET
1,3
COMMENTS
There is an obvious pattern here, but it is not known how long it will continue.
The cube roots (written in base 4) are 0, 1, 11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001 (coinciding with A056810 to this point).
LINKS
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]
FORMULA
Conjectures from Chai Wah Wu, Dec 25 2023: (Start)
a(n) = 1111*a(n-1) - 112110*a(n-2) + 1111000*a(n-3) - 1000000*a(n-4) for n > 6.
G.f.: x^2*(-7000000*x^4 + 6446000*x^3 - 336330*x^2 + 220*x + 1)/((x - 1)*(10*x - 1)*(100*x - 1)*(1000*x - 1)). (End)
CROSSREFS
Sequence in context: A226716 A076443 A278936 * A052076 A013795 A013860
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Oct 22 2015
EXTENSIONS
a(11) from Chai Wah Wu, Oct 23 2015
a(12)-a(14) from Chai Wah Wu, Sep 26 2017
STATUS
approved