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A052064
Cubes containing no palindromic substring except single digits.
6
0, 1, 8, 27, 64, 125, 216, 512, 729, 1728, 2197, 4096, 4913, 5832, 6859, 9261, 10648, 13824, 15625, 19683, 21952, 24389, 32768, 35937, 42875, 50653, 54872, 59319, 68921, 79507, 85184, 103823, 132651, 185193, 205379, 274625, 287496, 328509
OFFSET
1,3
COMMENTS
Sequence is probably finite.
Leading zeros in substring allowed so 52^2 = 140608 is rejected because 14{060}8 contains a palindromic substring.
LINKS
EXAMPLE
132651 (= 51^3) -> substrings 13, 32, 26, 65, 51, 132, 326, 265, 651, 1326, 3265, 2651, 13265, 32651 and 132651 are all non-palindromic.
MATHEMATICA
npsQ[n_]:=Count[Flatten[Table[Partition[IntegerDigits[n], i, 1], {i, 2, IntegerLength[ n]}], 1], _?(#==Reverse[#]&)]==0; Select[Range[ 0, 100]^3, npsQ] (* Harvey P. Dale, Dec 10 2016 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Jan 15 2000
EXTENSIONS
Offset changed to 1 by Sean A. Irvine, Oct 17 2019
STATUS
approved